Vladimir Mazya
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Vladimir Gilelevich Maz'ya (Russian: Владимир Гилелевич Мазья; born December 31, 1937)^{[1]}^{[2]}^{[3]} (the family name is sometimes transliterated as Mazya, Maz'ja or Mazja) is a Russian-born Swedish mathematician, hailed as "one of the most distinguished analysts of our time"^{[4]} and as "an outstanding mathematician of worldwide reputation",^{[5]} who strongly influenced the development of mathematical analysis and the theory of partial differential equations.^{[6]}^{[7]} His early achievements include: his work on Sobolev spaces, in particular the discovery of the equivalence between Sobolev and isoperimetric/isocapacitary inequalities (1960),^{[8]} his counterexamples related to Hilbert's 19th and Hilbert's 20th problem (1968),^{[9]} his solution, together with Yuri Burago, of a problem in harmonic potential theory (1967) posed by Riesz & Nagy (1955, chapter V, § 91), his extension of the Wiener regularity test to p–Laplacian and the proof of its sufficiency for the boundary regularity.^{[10]} Maz'ya solved V. Arnol'd's problem for the oblique derivative boundary value problem (1970) and F. John's problem on the oscillations of a fluid in the presence of an immersed body (1977). In recent years, he proved a Wiener's type criterion for higher order elliptic equations, together with M. Shubin solved a problem in the spectral theory of the Schrödinger operator formulated by Israel Gelfand in 1953,^{[11]} found necessary and sufficient conditions for the validity of maximum principles for elliptic and parabolic systems of PDEs and introduced the so–called approximate approximations. He also contributed to the development of the theory of capacities, nonlinear potential theory, the asymptotic and qualitative theory of arbitrary order elliptic equations, the theory of ill-posed problems, the theory of boundary value problems in domains with piecewise smooth boundary.
Biography
Life and academic career
Vladimir Maz'ya was born on 31 December 1937^{[2]} in a Jewish family.^{[12]} His father died in December 1941 at the World War II front,^{[2]}^{[12]}^{[13]} and all four grandparents died during the siege of Leningrad.^{[2]}^{[12]} His mother, a state accountant,^{[14]} chose to not remarry and dedicated her life to him:^{[12]} they lived on her meager salary in a 9 square meters room in a big communal apartment, shared with other four families.^{[12]}^{[15]} As a secondary school student, he repeatedly won the city's mathematics and physics olympiads^{[16]} and graduated with a gold medal.^{[17]}
In 1955, at the age of 18, Maz'ya entered the Mathematics and Mechanics Department of Leningrad University.^{[18]} Taking part to the traditional mathematical olympiad of the faculty, he solved the problems for both first year and second year students and, since he did not make this a secret, the other participants did not submit their solutions causing the invalidation of the contest by the jury which therefore did not award the prize.^{[13]} However, he attracted the attention of Solomon Mikhlin who invited him at his home, thus starting their lifelong friendship:^{[13]} and this friendship had a great influence on him, helping him develop his mathematical style more than anyone else. According to Gohberg (1999, p. 2),^{[19]} in the years to come, "Maz'ya was never a formal student of Mikhlin, but Mikhlin was more than a teacher for him. Maz’ya had found the topics of his dissertations by himself, while Mikhlin taught him mathematical ethics and rules of writing, referring and reviewing".^{[20]}
More details on the life of Vladimir Maz'ya, from his birth to the year 1968, can be found in his autobiography (Maz'ya 2014).
Maz'ya graduated from Leningrad University in 1960.^{[1]}^{[21]} The same year he gave two talks at Smirnov's seminar:^{[22]} their contents were published as a short report in the Proceedings of the USSR Academy of Sciences^{[23]}^{[24]} and later evolved in his "kandidat nauk" thesis, "Classes of sets and embedding theorems for function spaces",^{[25]} which was defended in 1962.^{[26]} In 1965 he earned the Doktor nauk degree, again from Leningrad University, defending the dissertation "Dirichlet and Neumann problems in Domains with irregular boundaries", when he was only 27.^{[27]} Neither the first nor his second thesis were written under the guidance of an advisor: Vladimir Maz'ya never had a formal scientific adviser, choosing the research problems he worked to by himself.^{[28]}
From 1960 up to 1986, he worked as a "research fellow"^{[29]} at the Research Institute of Mathematics and Mechanics of Leningrad University (RIMM), being promoted from junior to senior research fellow in 1965.^{[30]} From 1968 to 1978 he taught at the Leningrad Shipbuilding Institute, where he was awarded the title of "professor" in 1976.^{[31]} From 1986 to 1990 he worked to the Leningrad Section of the Blagonravov Research Institute of Mechanical Engineering of the USSR Academy of Sciences,^{[32]} where he created and directed the Laboratory of Mathematical Models in Mechanics and the Consulting Center in Mathematics for Engineers.^{[33]}
In 1978 he married Tatyana Shaposhnikova, a former doctoral student of Solomon Mikhlin, and they have a son, Michael:^{[34]} In 1990, they left the URSS for Sweden, where Prof. Maz'ya obtained the Swedish citizenship and started to work at Linköping University.^{[35]}
Currently, he is honorary Senior Fellow of Liverpool University and Professor Emeritus at Linköping University: he is also member of the editorial board of several mathematical journals.^{[36]}
Honors
In 1962 Maz'ya was awarded the "Young Mathematician" prize by the Leningrad Mathematical Society, for his results on Sobolev spaces:^{[25]} he was the first winner of the prize.^{[23]} In 1990 he was awarded an honorary doctorate from Rostock University.^{[37]} In 1999, Maz'ya received the Humboldt Prize.^{[37]}^{[38]} He was elected member of the Royal Society of Edinburgh in 2000,^{[39]} and of the Swedish Academy of Science in 2002.^{[37]} In March 2003, he, jointly with Tatyana Shaposhnikova, was awarded the Verdaguer Prize by the French Academy of Sciences.^{[40]} On 31 August 2004 he was awarded the Celsius Gold Medal, the Royal Society of Sciences in Uppsala's top award, "for his outstanding research on partial differential equations and hydrodynamics".^{[41]} He was awarded the Senior Whitehead Prize by the London Mathematical Society on 20 November 2009.^{[42]} In 2012 he was elected fellow of the American Mathematical Society.^{[43]} On October 30, 2013 he was elected foreign member of the Georgian National Academy of Sciences.^{[44]}
Starting from 1993, several conferences have been held to honor him: the first one, held in that year at the University of Kyoto, was a conference on Sobolev spaces.^{[45]} On the occasion of his 60th birthday in 1998, two international conferences were held in his honor: the one at the University of Rostock was on Sobolev spaces,^{[45]}^{[46]} while the other, at the École Polytechnique in Paris,^{[45]}^{[47]} was on the boundary element method. He was invited speaker at the International Mathematical Congress held in Beijing in 2002:^{[37]} his talk is an exposition on his work on Wiener–type criteria for higher order elliptic equations. Other two conferences were held on the occasion of his 70th birthday: "Analysis, PDEs and Applications on the occasion of the 70th birthday of Vladimir Maz'ya" was held in Rome,^{[48]} while the "Nordic – Russian Symposium in honour of Vladimir Maz'ya on the occasion of his 70th birthday" was held in Stockholm.^{[49]} On the same occasion, also a volume of the Proceedings of Symposia in Pure Mathematics was dedicated to him.^{[50]}
Work
Research activity
Because of Maz’ya’s ability to give complete solutions to problems which are generally considered as unsolvable, Fichera once compared Maz’ya with Santa Rita, the 14th century Italian nun who is the Patron Saint of Impossible Causes.
Maz'ya authored/coauthored more than 500 publications, including 20 research monographs. Several survey articles describing his work can be found in the book (Rossmann, Takáč & Wildenhain 1999a), and also the paper by Dorina and Marius Mitrea (2008) describes extensively his research achievements, so these references are the main ones in this section: in particular, the classification of the research work of Vladimir Maz'ya is the one proposed by the authors of these two references.
Theory of boundary value problems in nonsmooth domains
In one of his early papers, Maz'ya (1961) considers the Dirichlet problem for the following linear elliptic equation:^{[51]}^{[52]}
- (1) ${\mathcal {L}}u=\nabla (A(x)\nabla )u+\mathbf {b} (x)\nabla u+c(x)u=f\qquad x\in \Omega \subset \mathbf {R} ^{n}$
where
He proves the following a priori estimate
- (2) $\Vert u\Vert _{L_{s}(\Omega )}\leq K\left[\Vert f\Vert _{L_{r}(\Omega )}+\Vert u\Vert _{L(\Omega )}\right]$
for the weak solution u of equation 1, where K is a constant depending on n, s, r κ and other parameters but not depending on the moduli of continuity of the coefficients. The integrability exponents of the L_{p} norms in Estimate 2 are subject to the relations
- 1/s ≥ 1/r - 2/n for n/2 > r > 1,
- s is an arbitrary positive number for r = n/2,
the fist one of which answers positively to a conjecture proposed by Guido Stampacchia (1958, p. 237).^{[53]}
Teaching activity
The information on Vladimir Maz'ya's teaching work is mainly taken from his 1999 Curriculum vitae,^{[54]} published as (Rossmann, Takáč & Wildenhain 1999, p. 333), from the biographical informations contained in several papers of the book (Rossmann, Takáč & Wildenhain 1999a), from the survey paper (Mitrea & Mitrea 2008) and from the available student dissertations.^{[55]} Based on this information, a partial list of his doctoral students is reported below:
- Jan Åslund
- George (Bastay) Baravdish
- Jana Björn
- Stefan Eilertsen
- Nikolai V. Grachev
- Aben Aleksandrovich Khvoles
- Nikolai Germanovich Kuznetsov
- Tjavdar Ivanov
- Michael Langer
- Michael Livshits
Selected works
Papers
- Maz'ya, V. G. (1960), Классы областей и теоремы вложения функциональных пространств, Доклады Академии Наук СССР (in Russian), 133: 527–530, MR 0126152, Zbl 0114.31001, translated as Maz'ya, V. G. (1960), "Classes of domains and imbedding theorems for function spaces", Soviet Mathematics. Doklady, 1: 882–885, MR 0126152, Zbl 0114.31001.
- Maz'ya, V. G. (1961), Некторые оценки решений эллиптических уравнений второго порядка, Доклады Академии Наук СССР (in Russian), 137: 1057–1059, Zbl 0115.08701, translated as Maz'ya, V. G. (1961), "Some estimates for solutions of elliptic second-order equations", Soviet Mathematics. Doklady, 2: 413–415, Zbl 0115.08701.
- Maz'ya, V. G. (1968), Примеры нерегулярных решений квазилинейных эллиптических уравнений с аналитическими коэффициентами, Функциональный анализ и его приложения (in Russian), 2 (3): 53–57, MR 2020860, Zbl 0179.43601, translated in English as Maz'ya, V. G. (1968), "Examples of nonregular solutions of quasilinear elliptic equations with analytic coefficients", Functional Analysis and Its Applications, 2 (3): 230–234, doi:10.1007/BF01076124, MR 2020860, Zbl 0179.43601, (Subscription required (help)).
- Maz'ya, V. G. (1969), "О слабых решениях задач Дирихле и Неймана", Труды Московского математического общества (in Russian), 20: 137–172, MR 0259329, Zbl 0179.43302, translated in English as Maz'ya, V. G. (1971) [1969], "On weak solutions of the Dirichlet and Neumann problems", Transactions of the Moscow Mathematical Society, 20: 135–172, MR 0259329, Zbl 0226.35027.
- Maz'ya, Vladimir; Shubin, Mikhail (2005), "Discreteness of spectrum and positivity criteria for Schrödinger operators", Annals of Mathematics, 162 (2): 919–942, doi:10.4007/annals.2005.162.919, JSTOR 20159932, MR 2183285, Zbl 1106.35043, (Subscription required (help))
Books
- Burago, Yu. D.; Maz'ya, V. G. (1967), "Некоторые вопросы теории потенциала и теории функций для областей с нерегулярными границами" [Certain questions of potential theory and function theory for regions with irregular boundaries], Записки научных семинаров ЛОМИ (in Russian), 3: 3–152, MR 0227447, Zbl 0172.14903, translated in English as Burago, Yu. D.; Maz'ya, V. G. (1969), Potential Theory and Function Theory on Irregular Regions, Seminars in Mathematics, V. A. Steklov Mathematical Institute, Leningrad, Vol. 3, New York: Consultants Bureau, pp. vii+68.
- Gelman, I. W; Mazja, W. G. (1981), Abschätzungen für Differentialoperatoren im Halbraum [Estimates for differential operators in the half space], Mathematische Lehrbücher und Monogaphien, II. Albeitung: Mathematische Monographien (in German), 54, Berlin: Akademie-Verlag, p. 221, ISBN 3-7643-1275-0, MR 0644480, Zbl 0499.47028. A definitive monograph, giving a detailed study of a priori estimates of constant coefficient matrix differential operators defined on ℝ^{n}×(0,+∞], with n ≥ 1.
- Maz'ja, Vladimir G. (1985), Sobolev Spaces, Springer Series in Soviet Mathematics, Berlin–Heidelberg–New York: Springer-Verlag, pp. xix+486, ISBN 3-540-13589-8, MR 0817985, Zbl 0692.46023 (also available with ISBN 0-387-13589-8).
- Maz'ya, V. G.; Shaposhnikova, T. O. (1985), Theory of multipliers in spaces of differentiable functions, Monographs and Studies in Mathematics, 23, Boston – London – Melbourne: Pitman Publishing Inc., pp. xiii+344, ISBN 0-273-08638-3, MR 0785568, Zbl 0645.46031.
- Maz'ya, V. G. (1991), "Boundary Integral Equations", in Maz'ya, V. G.; Nikol'skiǐ, S. M., Analysis IV, Encyclopaedia of Mathematical Sciences, 27, Berlin–Heidelberg–New York: Springer-Verlag, pp. 127–222, ISBN 0-387-51997-1, MR 1098507, Zbl 0780.45002 (also available as ISBN 3-540-51997-1).
- Maz'ya, Vladimir G.; Poborchi, Sergei V. (1997), Differentiable Functions on Bad Domains, Singapore–New Jersey–London–Hong Kong: World Scientific, pp. xx+481, ISBN 981-02-2767-1, MR 1643072, Zbl 0918.46033.
- Kozlov, V. A.; Maz'ya, V. G.; Rossmann, J. (1997), Elliptic Boundary Value Problems in Domains with Point Singularities, Mathematical Surveys and Monographs, 52, Providence, RI: American Mathematical Society, pp. x+414, ISBN 0-8218-0754-4, MR 1469972, Zbl 0947.35004.
- Maz'ya, Vladimir; Shaposhnikova, Tatyana (1998), Jacques Hadamard, a Universal Mathematician, History of Mathematics, 14, Providence, RI and London: American Mathematical Society and London Mathematical Society, pp. xxv+574, ISBN 0-8218-0841-9, MR 1611073, Zbl 0906.01031. There are also two revised and expanded editions: the French translation Maz'ya, Vladimir; Shaposhnikova, Tatyana (January 2005) [1998], Jacques Hadamard, un mathématicien universel, Sciences & Histoire (in French), Paris: EDP Sciences, p. 554, ISBN 2-86883-707-7, and the (further revised and expanded) Russian translation Мазья, В. Г.; Шапошникова, Т. О. (2008) [1998], Жак Адамар Легенда Математики (in Russian), Москва: ИздателЬство МЦНМО, p. 528, ISBN 978-5-94057-083-7.
- Kozlov, Vladimir; Maz'ya, Vladimir (1999), Differential Equations with Operator Coefficients, Springer Monographs in Mathematics, Berlin–Heidelberg–New York: Springer-Verlag, pp. XV+442, ISBN 3-540-65119-5, MR 1729870, Zbl 0920.35003.
- Kozlov, V. A.; Maz'ya, V. G.; Movchan, A. B. (1999), Asymptotic Analysis of Fields in Multi-Structures, Oxford Mathematical Monographs, Oxford: Oxford University Press, pp. xvi+282, ISBN 978-0-19-851495-4, MR 1860617, Zbl 0951.35004.
- Maz'ya, Vladimir G.; Nazarov, Serguei; Plamenevskij, Boris (2000), Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Volume I, Operator Theory: Advances and Applications, 110, Birkhäuser Verlag, pp. XXIV+435, ISBN 3-7643-6397-5, MR 1779977, Zbl 1127.35300.
- Maz'ya, Vladimir G.; Nazarov, Serguei; Plamenevskij, Boris (2000), Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains. Volume II, Operator Theory: Advances and Applications, 112, Birkhäuser Verlag, pp. XXIV+323, ISBN 3-7643-6398-3, MR 1779978, Zbl 1127.35301.
- Kozlov, V. A.; Maz'ya, V. G.; Rossmann, J. (2001), Spectral Problems Associated with Corner Singularities of Solutions to Elliptic Equations, Mathematical Surveys and Monographs, 85, Providence, RI: American Mathematical Society, pp. x+436, ISBN 0-8218-2727-8, MR 1788991, Zbl 0965.35003.
- Kuznetsov, N.; Maz'ya, V.; Vainberg, B. (2002), Linear Water Waves. A Mathematical Approach., Cambridge: Cambridge University Press, pp. xviii+513, ISBN 0-521-80853-7, MR 1925354, Zbl 0996.76001.
- Kresin, Gershon; Maz'ya, Vladimir G. (2007), Sharp Real-Part Theorems. A Unified Approach (PDF), Lecture Notes in Mathematics, 1903, Berlin–Heidelberg–New York: Springer-Verlag, pp. xvi+140, ISBN 978-3-540-69573-8, MR 2298774, Zbl 1117.30001.
- Maz'ya, Vladimir; Schmidt, Gunther (2007), Approximate approximations (PDF), Mathematical Surveys and Monographs, 141, Providence, RI: American Mathematical Society, pp. xiv+349, ISBN 978-0-8218-4203-4, MR 2331734, Zbl 1120.41013.
- Maz'ya, Vladimir G.; Shaposhnikova, Tatyana O. (2009) [1985], Theory of Sobolev multipliers. With applications to differential and integral operators, Grundlehren der Mathematischen Wissenschaft, 337, Berlin–Heidelberg–New York: Springer-Verlag, pp. xiii+609, ISBN 978-3-540-69490-8, MR 2457601, Zbl 1157.46001.
- Maz'ya, Vladimir; Rossmann, Jürgen (2010), Elliptic Equations in Polyhedral Domains, Mathematical Surveys and Monographs, 162, Providence, RI: American Mathematical Society, pp. viii+608, ISBN 978-0-8218-4983-5, MR 2641539, Zbl 1196.35005.
- Maz'ya, Vladimir G.; Soloviev, Alexander A. (2010), Boundary Integral Equations on Contours with Peaks, Operator Theory: Advances and Applications, 196, Basel: Birkhäuser Verlag, pp. vii+342, ISBN 978-3-0346-0170-2, MR 2584276, Zbl 1179.45001.
- Maz'ya, Vladimir G. (2011) [1985], Sobolev Spaces. With Applications to Elliptic Partial Differential Equations., Grundlehren der Mathematischen Wissenschaften, 342 (2nd revised and augmented ed.), Berlin–Heidelberg–New York: Springer Verlag, pp. xxviii+866, ISBN 978-3-642-15563-5, MR 2777530, Zbl 1217.46002.
- Kresin, Gershon; Maz'ya, Vladimir (2012), Maximum Principles and Sharp Constants for Solutions of Elliptic and Parabolic Systems, Mathematical Surveys and Monographs, 183, Providence, RI: American Mathematical Society, pp. vii+317, ISBN 978-0-8218-8981-7, MR 2962313, Zbl 1255.35001.
- Maz'ya, Vladimir (2014), Differential equations of my young years, Basel: Birkhäuser Verlag, pp. xiii+191, ISBN 978-3-319-01808-9, MR 3288312, Zbl 1303.01002 (also published with ISBN 978-3-319-01809-6).
See also
Notes
- ^ ^{a} ^{b} See (Fomin & Shilov 1970, p. 824).
- ^ ^{a} ^{b} ^{c} ^{d} See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 189), (Bonnet, Sändig & Wendland 1999, p. 3) and (Mitrea & Mitrea 2008, p. vii).
- ^ See also (Anolik et al. 2008, p. 287).
- ^ (Mitrea & Mitrea 2008, p. viii).
- ^ (Havin 2014, p. v).
- ^ (Agranovich et al. 2008, p. 189), (Laptev 2010, p. v), (Chillingworth 2010).
- ^ (Bonnet, Sändig & Wendland 1999, p. 3), (Mitrea & Mitrea 2008, p. vii), (Anolik et al. 2008, p. 287), (Movchan et al. 2015, p. 273).
- ^ (Maz'ya 1960).
- ^ (Maz'ya 1968), (Giaquinta 1983, p. 59), (Giusti 1994, p. 7, footnote 7, and p. 353) (p. 6, footnote 7, and p. 343 of the English translation).
- ^ The necessity of the condition was an open problem until 1993, when it was proved by Kilpeläinen & Malý (1994).
- ^ (Maz'ya & Shubin 2005). For a brief description of this and related researches, see (Mitrea & Mitrea 2008, p. xiv).
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} See (Eidus et al. 1997, p. 1).
- ^ ^{a} ^{b} ^{c} See (Gohberg 1999, p. 2).
- ^ See (Agranovich et al. 2003, p. 239) and (Mitrea & Mitrea 2008, p. vii).
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 189) and (Mitrea & Mitrea 2008, p. viii).
- ^ See (Agranovich et al. 2008, p. 189), (Bonnet, Sändig & Wendland 1999, p. 3) and (Mitrea & Mitrea 2008, p. viii).
- ^ See (Agranovich et al. 2008, p. 189), (Eidus et al. 1997, p. 2) and (Mitrea & Mitrea 2008, p. viii).
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 189), Bonnet, Sändig & Wendland (1999, p. 3) and (Eidus et al. 1997, p. 2).
- ^ Also reported by Mitrea & Mitrea (2008, p. viii).
- ^ See also short accounts of their friendship in (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 189), (Anolik et al. 2008, p. 287), (Bonnet, Sändig & Wendland 1999, p. 3) and (Eidus et al. 1997, p. 2).
- ^ See (Agranovich et al. 2008, p. 189), (Anolik et al. 2008, p. 287) and (Mitrea & Mitrea 2008, p. viii).
- ^ According to Agranovich et al. (2008, p. 189): Mitrea & Mitrea (2008, p. viii) are less precise, simply referring of "talks" he gave, while Anolik et al. (2008, p. 287) cite only a single talk.
- ^ ^{a} ^{b} See (Agranovich et al. 2008, p. 189).
- ^ See the books (Maz'ja 1986) and (Maz'ya 2011) for a complete analysis of his results.
- ^ ^{a} ^{b} (Maz'ya 1960). See (Agranovich et al. 2008, p. 189), (Anolik et al. 2008, p. 287), (Eidus et al. 1997, p. 2) and (Mitrea & Mitrea 2008, p. viii): Agranovich et al. (2008, p. 189) refer that "In their reviews, the opponents and the external reviewer noted that the level of the work far exceeded the requirements of the Higher Certification Commission for Ph.D. theses, and his work was recognized as outstanding at the thesis defence in the Academic Council of Moscow State University".
- ^ See (Agranovich et al. 2008, p. 189), (Anolik et al. 2008, p. 287), (Eidus et al. 1997, p. 2) and Mitrea & Mitrea (2008, p. viii).
- ^ According to (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190), (Anolik et al. 2008, p. 287), Bonnet, Sändig & Wendland (1999, p. 3),(Eidus et al. 1997, p. 2) and Mitrea & Mitrea (2008, p. viii): Fomin & Shilov (1970, p. 824) give a different year, stating that he earned the "Doctor nauk" degree in 1967.
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, pp. 189–190), (Anolik et al. 2008, p. 287), (Gohberg 1999, p. 2) and Mitrea & Mitrea (2008, p. viii).
- ^ Russian: научный сотрудник: see (Agranovich et al. 2003, p. 239), (Anolik et al. 2008, p. 287), (Eidus et al. 1997, p. 2) and Mitrea & Mitrea (2008, p. viii).
- ^ Precisely, he become "старший научный сотрудник", abbreviated as "ст. науч. сотр.", according to Fomin & Shilov (1970, p. 824), the only source giving a precise date for this career advancement.
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190), (Anolik et al. 2008, p. 287), (Eidus et al. 1997, p. 2) and Mitrea & Mitrea (2008, p. viii): a different version is reported by Bonnet, Sändig & Wendland (1999, p. 3), whom state that he become professor of Applied Mathematics in 1971 but do not give any other detail about his teaching activity.
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190), (Anolik et al. 2008, p. 287) and Mitrea & Mitrea (2008, pp. viii–ix).
- ^ According to (Agranovich et al. 2003, p. 239): (Agranovich et al. 2008, p. 190) states precisely that he was the chairman of the laboratory for several years, while (Anolik et al. 2008, p. 287) does simply state that it was its head.
- ^ The only source briefly mentioning the composition of his household is (Bonnet, Sändig & Wendland 1999, p. 3).
- ^ See (Agranovich et al. 2003, p. 239), (Anolik et al. 2008, p. 287), (Bonnet, Sändig & Wendland 1999, p. 3), (Eidus et al. 1997, p. 2) and (Mitrea & Mitrea 2008, pp. viii–ix).
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190) and (Anolik et al. 2008, p. 287).
- ^ ^{a} ^{b} ^{c} ^{d} See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190), (Anolik et al. 2008, p. 287) and (Mitrea & Mitrea 2008, pp. ix).
- ^ See (O'Connor & Robertson 2009).
- ^ See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190), (Anolik et al. 2008, p. 287) and (Mitrea & Mitrea 2008, pp. ix), and also the list of RSE members.
- ^ For his work on the biography of Jacques Hadamard. See the short announcements of the French Academy of Sciences (2009).
- ^ Sundelof (2003, p. 33) precisely states:-"Celsiusmedaljen i guld, Societetens främsta utmärkelse, har tilldelats professor Vladimir Maz'ya, Linköping, för hans framstående forskning rörande partiella differentialkvationer och hydrodynamik". See also the brief announce (AMS 2005, p. 549).
- ^ (Chillingworth 2010), (LMS 2010, p. 334): there is also the brief announce in (AMS 2010, p. 1120).
- ^ See the list of AMS fellows.
- ^ See his membership diploma, available from the Georgian National Academy web site.
- ^ ^{a} ^{b} ^{c} See (Agranovich et al. 2003, p. 239), (Agranovich et al. 2008, p. 190) and (Mitrea & Mitrea 2008, p. ix).
- ^ The conference proceedings are published in two books, The Maz'ya Anniversary Collection: Volume 1 (1999) and The Maz'ya Anniversary Collection: Volume 2 (1999).
- ^ See also Bonnet, Sändig & Wendland (1999, p. 3). The whole conference proceedings are published in the book (Mathematical Aspects of Boundary Element Methods 1999).
- ^ See Mitrea & Mitrea (2008, p. ix) and also the conference web site (2008). The proceedings were published under the editorship of Cialdea, Lanzara & Ricci (2009).
- ^ See Mitrea & Mitrea (2008, p. ix) and also the conference web site (2008).
- ^ See (Mitrea & Mitrea 2008a).
- ^ (Rossmann 1999, pp. 57–58). See also (Stampacchia 1963, p. 408) for a brief remark.
- ^ For a survey of this problem, including details on several contributions to its study, see (Miranda 1970, §30, pp. 121–128).
- ^ Maz'ya (1961, p. 413).
- ^ And also from the curriculum vitae available from his home page (retrieved February 2014).
- ^ See for example (Khvoles 1975, p.2 of frontmatter), (Kuznetsov & Vainberg 1999, p. 17), (Elschner 1999, p. 46) and (Mitrea & Mitrea 2008, p. x).
References
Biographical and general references
- Agranovich, M. S.; Burago, Yu. D.; Khavin, V. P.; Kondrat'ev, V. A.; Maslov, V. P.; Nikol'skii, S. M.; Reshetnyak, Yu. G.; Shubin, M. A.; Vainberg, B. R.; Volevich, L. I. (2003), "Vladimir Gilelevich Maz'ya, On the occasion of his 65th birthday", Russian Journal of Mathematical Physics, 10 (3): 239–244. A biographical paper written on the occasion of Maz'ya 65th birthday: a freely accessible version is available here from Prof. Maz'ya web site.
- Agranovich, M. S.; Burago, Yu. D.; Vainberg, B. R.; Vishik, M. I.; Gindikin, S. G.; Kondrat'ev, V. A.; Maslov, V. P.; Poborchii, S. V.; et al. (2008), "Vladimir Gilelevich Maz'ya (on his 70th birthday)", Russian Mathematical Surveys, 63 (1): 189–196, doi:10.1070/RM2008v063n01ABEH004511, MR 2406192, Zbl 1221.01098, (Subscription required (help)). A biographical paper written on the occasion of Maz'ya 70th birthday (a freely accessible English translation is available here from Prof. Maz'ya web site), translated from the (freely accessible) Russian original "Владимир Гилелевич Мазья (к 70-летию со дня рождения)", Russian Mathematical Surveys, 63 (1 (379)): 183–189, 2008, MR 2406192, Zbl 1221.01098.
- AMS (2005), "Mathematics People" (PDF), Notices of the American Mathematical Society, 52 (5): 432–438.
- AMS (2009), "Mathematics People" (PDF), Notices of the American Mathematical Society, 56 (9): 1119–1121.
- AMS (1 November 2012), List of Fellows of the American Mathematical Society, retrieved 13 November 2012.
- Anolik, M. V.; Burago, Yu. D.; Dem'yanovich, Yu. K.; Kislyakov, S. V.; Khavin, V. P.; Leonov, G. A.; Morozov, N. F.; Poborchii, S. V.; Ural'tseva, N. N.; Shirokov, N. A. (2008), "Vladimir Gilelevich Maz'ya (On the Occasion of His 70th Anniversary)", Vestnik St. Petersburg University: Mathematics, 41 (4): 287–289, doi:10.3103/S1063454108040018, MR 2485391, Zbl 1172.01313, (Subscription required (help)). Another biographical paper written on the occasion of Maz'ya 70th birthday: a freely accessible version is available here from Prof. Maz'ya web site.
- Bonnet, Marc; Sändig, Anna-Margarete; Wendland, Wolfgang (1999), "Dedication", in Bonnet, M.; Sändig, A.-M.; Wendland, W. L., Mathematical Aspects of Boundary Element Methods, dedicated to Vladimir Maz'ya on the occasion of his 60th birthday, Chapman & Hall/CRC Research Notes in Mathematics, 414, Boca Raton/London: Chapman & Hall/CRC, pp. 3–6, ISBN 1-58488-006-6, MR 1726554, Zbl 0924.00038. Proceedings of the minisymposium held at the École Polytechnique, Palaiseau, May 25–29, 1998.
- Chillingworth, David (February 2010), "LMS Annual General Meeting – 20 November 2009", London Mathematical Society Newsletter, No. 389.
- Cialdea, Alberto; Lanzara, Flavia; Ricci, Paolo Emilio (2009), "On the Occasion of the 70th Birthday of Vladimir Maz'ya" (PDF), in Cialdea, Alberto; Lanzara, Flavia; Ricci, Paolo Emilio, Analysis, partial differential equations and applications. The Vladimir Maz'ya anniversary volume. Selected lectures from the International Workshop held at Sapienza University, Rome, June 30–July 3, 2008., Operator Theory: Advances and Applications, 193, Basel: Birkhäuser Verlag, pp. ix–xvii, doi:10.1007/978-3-7643-9898-9, ISBN 978-3-7643-9897-2, MR 2760868, Zbl 1173.35006.
- Eidus, D.; Khvoles, A.; Kresin, G.; Merzbach, E.; Prössdorf, S.; Shaposhnikova, T.; Sobolevskii, P.; Solomiak, M. (1997), "Mathemathical Work of Vladimir Maz'ya (on the occasion of his 60th birthday)", Functional Differential Equations, 4 (1–2): 3–11, MR 1491785, Zbl 0896.35002.
- Fomin, S. V.; Shilov, G. E., eds. (1970), Математика в СССР 1958–1967 [Mathematics in the USSR 1958–1967] (in Russian), Том второй: Биобиблиография выпуск второй М–Я, Москва: Издательство "Наука", p. 762, MR 0250816, Zbl 0199.28501. A two–volume continuation of the opus "Mathematics in the USSR during its first forty years 1917–1957", describing the developments of Soviet mathematics during the period 1958–1967. Precisely it is meant as a continuation of the second volume of that work and, as such, is titled "Biobibliography" (evidently an acronym of biography and bibliography). It includes new biographies (when possible, brief and complete) and bibliographies of works published by new Soviet mathematicians during that period, and updates on the work and biographies of scientist included in the former volume, alphabetically ordered with respect to author's surname.
- French Academy of Sciences (2009), Prix Verdaguer (PDF) (in French), retrieved May 8, 2011. A list of the winners of the Verdaguer Prize in PDF format, including short motivations for the awarding.
- Georgian National Academy of Sciences (30 October 2013), Membership diploma (PDF) (in Georgian and English). The membership diploma awarded to Vladimir Maz'ya on the occasion of his election as foreign member of the Georgian National Academy of Sciences.
- Gohberg, Israel (1999), "Vladimir Maz'ya: Friend and Mathematician. Recollections", in Rossman, Jürgen; Takáč, Peter; Wildenhain, Günther, The Maz'ya anniversary collection. Vol. 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Based on talks given at the conference, Rostock, Germany, August 31 – September 4, 1998, Operator Theory. Advances and Applications, 109, Basel: Birkhäuser Verlag, pp. 1–5, ISBN 978-3-7643-6201-0, MR 1747861, Zbl 0939.01018.
- Havin, V. P. (2014), "Foreword", in Maz'ya, Vladimir, Differential equations of my young years, Basel: Birkhäuser Verlag, pp. v–vii, doi:10.1007/978-3-319-01809-6, ISBN 978-3-319-01808-9, MR 3288312, Zbl 1303.01002.
- Khvoles, Aben Aleksandovich (1975), Сингулярные интегральные уравнения в пространствах C_{ω}(M) [Singular integral equations on the space C_{ω}(M)], Автореферат диссертации на соискание учёной кандидата физико-математических наук (in Russian), Тбилиси: Академяя Наук Грузинскои ССР–Тбилисский Ордена Трудового Красного Знамени математический институт им. А. М. Размадзе. The summary of the kandidat nauk thesis of Aben Khvoles, one of the doctoral students of Vladimir Maz'ya.
- Mitrea, Dorina; Mitrea, Marius (2008), "On the Scientific Work of V. G. Maz'ya: a personalized account" (PDF), in Mitrea, Dorina; Mitrea, Marius, Perspectives in Partial Differential Equations, Harmonic Analysis and Applications. A volume in Honor of Vladimir G Maz'ya's 70th Birthday., Proceedings of Symposia in Pure Mathematics, 79, Providence, RI: American Mathematical Society, pp. vii–xvii, ISBN 978-0-8218-4424-3, MR 1500279, Zbl 1153.01330.
- London Mathematical Society (2010), "Prizewinners 2009", Bulletin of the London Mathematical Society, 42: 332–340, doi:10.1112/blms/bdp136 – via EBSCO, (Subscription required (help))
- Movchan, A.; Safarov, Yu.; Sobolev, A.; Vassiliev, D. (May 2015), "In honour of Professor Vladimir Maz'ya on the occasion of his 75th birthday", Mathematika, 61 (2): 273–275, doi:10.1112/S0025579315000145, ISSN 0025-5793, MR 3343052, Zbl 1314.01024 (e–ISSN 2041-7942).
- Rossmann, Jürgen; Takáč, Peter; Wildenhain, Günther, eds. (1999), "Curriculum vitae of Vladimir Maz'ya" (PDF), The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Papers from the Conference on Functional Analysis, Partial Differential Equations, and Applications held at the University of Rostock, Rostock, August 31–September 4, 1998., Operator Theory: Advances and Applications, 109, Birkhäuser Verlag, pp. 331–333.
- Royal Society of Edinburgh (2008), RSE fellows (PDF), retrieved 30 April 2012.
- Sundelöf, Lars-Olof (2004), "Presentation av priser och belönigar år 2004", Årsbok 2004 (in Swedish), Uppsala: Kungl. Vetenskaps-Societeten i Uppsala, pp. 31–39, ISSN 0348-7849. The "Presentation of prizes and awards" speech given by the Secretary of the Royal Society of Sciences in Uppsala, written in the "yearbook 2004", on the occasion of the awarding of the Society prizes to prof. V. Maz'ya and to other 2004 winners.
Scientific references
- Elschner, Johannes (1999), "The work of Vladimir Maz'ya on integral and pseudodifferential operators", in Rossmann, Jürgen; Takáč, Peter; Wildenhain, Günther, The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Papers from the Conference on Functional Analysis, Partial Differential Equations, and Applications held at the University of Rostock, Rostock, August 31–September 4, 1998., Operator Theory: Advances and Applications, 109, Birkhäuser Verlag, pp. 35–52, doi:10.1007/978-3-0348-8675-8_4, MR 1747864, Zbl 0940.35008, (Subscription required (help)).
- Giaquinta, Mariano (1983), Multiple integrals in the calculus of variations and nonlinear elliptic systems, Annals of Mathematics Studies, 105, Princeton, NJ: Princeton University Press, pp. vii+297, ISBN 0-691-08330-4, MR 0717034, Zbl 0516.49003.
- Giusti, Enrico (1994), Metodi diretti nel calcolo delle variazioni, Monografie Matematiche (in Italian), Bologna: Unione Matematica Italiana, pp. VI+422, MR 1707291, Zbl 0942.49002, translated in English as Giusti, Enrico (2003), Direct Methods in the Calculus of Variations, River Edge, NJ – London – Singapore: World Scientific Publishing, pp. viii+403, ISBN 981-238-043-4, MR 1962933, Zbl 1028.49001.
- Kilpeläinen, Tero; Malý, Jan (1994), "The Wiener test and potential estimates for quasilinear elliptic equations", Acta Mathematica, 172 (1): 137–161, doi:10.1007/BF02392793, MR 1264000, Zbl 0820.35063, (Subscription required (help)).
- Kuznetsov, N. G.; B. R., Vainberg (1999), "Maz'ya's works in the linear theory of water waves", in Rossmann, Jürgen; Takáč, Peter; Wildenhain, Günther, The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Papers from the Conference on Functional Analysis, Partial Differential Equations, and Applications held at the University of Rostock, Rostock, August 31–September 4, 1998., Operator Theory: Advances and Applications, 109, Birkhäuser Verlag, pp. 17–34, doi:10.1007/978-3-0348-8675-8_3, MR 1747863, Zbl 0937.35002, (Subscription required (help)).
- Miranda, Carlo (1970) [1955], Partial Differential Equations of Elliptic Type, Ergebnisse der Mathematik und ihrer Grenzgebiete – 2 Folge, Band 2, translated by Motteler, Zane C. (2nd Revised ed.), Berlin – Heidelberg – New York: Springer Verlag, pp. XII+370, doi:10.1007/978-3-642-87773-5, ISBN 978-3-540-04804-6, MR 0284700, Zbl 0198.14101, (Subscription required (help)).
- Riesz, Frigyes; Sz.-Nagy, Béla (1955), Functional analysis, translated by Boron, Leo F., Frederick Ungar Publishing Co., pp. XII+468, MR 0071727, Zbl 0070.10902.
- Rossmann, Jürgen (1999), "Contributions of V. Maz'ya to the theory of boundary value problems in nonsmooth domains", in Rossmann, Jürgen; Takáč, Peter; Wildenhain, Günther, The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Papers from the Conference on Functional Analysis, Partial Differential Equations, and Applications held at the University of Rostock, Rostock, August 31–September 4, 1998., Operator Theory: Advances and Applications, 109, Birkhäuser Verlag, pp. 53–98, doi:10.1007/978-3-0348-8675-8_5, MR 1747865, Zbl 0936.35006.
- Stampacchia, Guido (1958), "Contributi alla regolarizzazione delle soluzioni dei problemi al contorno per equazioni del secondo ordine ellittiche" [Contributions to the regularization of the solutions to boundary value problems for second order elliptic equations], Annali della Scuola Normale Superiore di Pisa. Classe di Scienze, Serie 3 (in Italian), 12 (3): 223–245, MR 0125313, Zbl 0082.09701.
- Stampacchia, Guido (1963), "Second order elliptic equations and boundary value problems" (PDF), Proceedings of the International Congress of Mathematicians, 15–22 August 1962, Stockholm, ICM Proceedings, 1962, Vol. 1, Stockholm: Almqvist & Wiksells, pp. 405–413, MR 0176198, Zbl 0137.06803.
Publications and conferences and dedicated to Vladimir Maz'ya
- "Analysis, PDEs and Applications, Conference on the occasion of the 70th birthday of Vladimir Maz'ya". University of Rome. June 30 – July 3, 2008. Retrieved 16 September 2012..
- Bonnet, M.; Sändig, A.–M.; Wendland, W. L., eds. (1999), Mathematical Aspects of Boundary Element Methods, dedicated to Vladimir Maz'ya on the occasion of his 60th birthday, Chapman & Hall/CRC Research Notes in Mathematics, 414, Boca Raton/London: Chapman & Hall/CRC, p. 305, ISBN 1-58488-006-6, MR 1726554, Zbl 0924.00038. Proceedings of the minisymposium held at the École Polytechnique, Palaiseau, May 25–29, 1998.
- Laptev, Ari, ed. (2010), Around the research of Vladimir Maz’ya. I. Function spaces, International Mathematical Series (New York), 11, New York/Novosibirsk: Springer Verlag/Tamara Rozhkovskaya Publisher, pp. xxi+395, doi:10.1007/978-1-4419-1341-8, ISBN 978-1-4419-1340-1, ISSN 1571-5485, MR 2676166, Zbl 1180.47001 (also published with ISBN 978-1-4614-2547-2; ISBN 978-1-4419-1341-8; and ISBN 978-5-9018-7341-0).
- Cialdea, Alberto; Lanzara, Flavia; Ricci, Paolo Emilio, eds. (2009), Analysis, partial differential equations and applications. The Vladimir Maz'ya anniversary volume. Selected lectures from the International Workshop held at Sapienza University, Rome, June 30–July 3, 2008., Operator Theory: Advances and Applications, 193, Basel: Birkhäuser Verlag, pp. ix–xvii, doi:10.1007/978-3-7643-9898-9, ISBN 978-3-7643-9897-2, MR 2760868, Zbl 1173.35006.
- AA. VV. (May 2015), "Issue dedicated to Vladimir Maz'ya", Mathematika, 61 (2): 273–500, doi:10.1112/S0025579315000030, ISSN 0025-5793, MR 3343052, Zbl 1314.01024 (e–ISSN 2041-7942).
- Laptev, Ari, ed. (2010a), Around the research of Vladimir Maz’ya. II. Partial Differential Equations, International Mathematical Series (New York), 12, New York/Novosibirsk: Springer Verlag/Tamara Rozhkovskaya Publisher, pp. xxii+385, doi:10.1007/978-1-4419-1343-2, ISBN 978-1-4419-1342-5, ISSN 1571-5485, MR 2664211, Zbl 1180.47002 (also published with ISBN 978-1-4614-2548-9; ISBN 978-1-4419-1343-2; and ISBN 978-5-9018-7342-7).
- Laptev, Ari, ed. (2010b), Around the research of Vladimir Maz’ya. III. Analysis and applicationsn spaces, International Mathematical Series (New York), 13, New York/Novosibirsk: Springer Verlag/Tamara Rozhkovskaya Publisher, pp. xxi+388, doi:10.1007/978-1-4419-1345-6, ISBN 978-1-4419-1344-9, ISSN 1571-5485, MR 2664210, Zbl 1180.47003 (also published with ISBN 978-1-4614-2551-9; ISBN 978-1-4419-1345-6; and ISBN 978-5-9018-7343-4).
- Mitrea, Dorina; Mitrea, Marius, eds. (2008a), Perspectives in Partial Differential Equations, Harmonic Analysis and Applications. A volume in Honor of Vladimir G Maz'ya's 70th Birthday., Proceedings of Symposia in Pure Mathematics, 79, Providence, RI: American Mathematical Society, pp. vi+423, ISBN 978-0-8218-4424-3, MR 1500279, Zbl 1149.43002.
- Rossmann, Jürgen; Takáč, Peter; Wildenhain, Günther, eds. (1999a), The Maz'ya Anniversary Collection: Volume 1: On Maz'ya's work in functional analysis, partial differential equations and applications. Papers from the Conference on Functional Analysis, Partial Differential Equations, and Applications held at the University of Rostock, Rostock, August 31–September 4, 1998., Operator Theory: Advances and Applications, 109, Birkhäuser Verlag, pp. xii+364, doi:10.1007/978-3-0348-8675-8, ISBN 3-7643-6201-4, MR 1747860, Zbl 0923.00034.
- Rossmann, Jürgen; Takáč, Peter; Wildenhain, Günther, eds. (1999b), The Mazʹya anniversary collection. Vol. 2. Rostock Conference on Functional Analysis, Partial Differential Equations and Applications. Papers from the conference held at the University of Rostock, Rostock, August 31–September 4, 1998., Operator Theory: Advances and Applications, 110, Birkhäuser Verlag, pp. xvi+352, doi:10.1007/978-3-0348-8672-7, ISBN 3-7643-6202-2, MR 1747883, Zbl 0923.00035.
- "Nordic – Russian Symposium in honour of Vladimir Maz'ya on the occasion of his 70th birthday". Department of mathematics – KTH. 25–27 August 2008. Retrieved 16 September 2012..
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