Vladimir Mazya

Life and academic career Vladimir Maz'ya was born on 31 December 1937 His father died in December 1941 at the World War II front, and all four grandparents died during the siege of Leningrad. chose to not remarry and dedicated her life to him: As a secondary school student, he repeatedly won the city's mathematics and physics olympiads and graduated with a gold medal. In 1955, at the age of 18, Maz'ya entered the Mathematics and Mechanics Department of Leningrad University. 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. 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''". More details on the life of Vladimir Maz'ya, from his birth to the year 1968, can be found in his autobiography . Maz'ya graduated from Leningrad University in 1960. The same year he gave two talks at Smirnov's seminar: their contents were published as a short report in the Proceedings of the USSR Academy of Sciences and later evolved in his "Candidate of Sciences" thesis, "Classes of sets and embedding theorems for function spaces", which was defended in 1962. In 1965 he earned the Doctor of Sciences degree, again from Leningrad University, defending the dissertation "Dirichlet and Neumann problems in Domains with irregular boundaries", when he was only 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. From 1960 up to 1986, he worked as a "research fellow" at the Research Institute of Mathematics and Mechanics of Leningrad University (RIMM), being promoted from junior to senior research fellow in 1965. From 1968 to 1978 he taught at the , where he was awarded the title of "professor" in 1976. From 1986 to 1990 he worked to the Leningrad Section of the of the USSR Academy of Sciences, where he created and directed the Laboratory of Mathematical Models in Mechanics and the Consulting Center in Mathematics for Engineers. In 1978 he married Tatyana Shaposhnikova, a former doctoral student of Solomon Mikhlin, and they have a son, Michael: In 1990, they left the URSS for Sweden, where Prof. Maz'ya obtained the Swedish citizenship and started to work at Linköping University. 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. Honors In 1962 Maz'ya was awarded the "Young Mathematician" prize by the Leningrad Mathematical Society, for his results on Sobolev spaces: In 1999, Maz'ya received the Humboldt Prize. He was elected member of the Royal Society of Edinburgh in 2000, and of the Swedish Academy of Science in 2002. 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". He was awarded the Senior Whitehead Prize by the London Mathematical Society on 20 November 2009. In 2012 he was elected fellow of the American Mathematical Society. On 30 October 2013 he was elected foreign member of the Georgian National Academy of Sciences. 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. 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, while the other, at the École Polytechnique in Paris, was on the boundary element method. He was invited speaker at the International Mathematical Congress held in Beijing in 2002: while the "''Nordic – Russian Symposium in honour of Vladimir Maz'ya on the occasion of his 70th birthday''" was held in Stockholm. On the same occasion, also a volume of the Proceedings of Symposia in Pure Mathematics was dedicated to him. On the occasion of his 80th birthday, a "Workshop on Sobolev Spaces and Partial Differential Equations" was held on 17–18 May 2018 was held at the Accademia Nazionale dei Lincei to honor him. On the 26–31 May 2019, the international conference "Harmonic Analysis and PDE" was held in his honor at the Holon Institute of Technology. ==Work==

Research activity Maz'ya authored/coauthored more than 500 publications, including 20 research monographs. Several survey articles describing his work can be found in the book , 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. He is also the author of Seventy (Five) Thousand Unsolved Problems in Analysis and Partial Differential Equations which collects problems he considers to be important research directions in the field Theory of boundary value problems in nonsmooth domains In one of his early papers, considers the Dirichlet problem for the following linear elliptic equation: :\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 • is a bounded region in the –dimensional euclidean space • is a matrix whose first eigenvalue is not less than a fixed positive constant and whose entries are functions sufficiently smooth defined on , the closure of . • , and are respectively a vector-valued function and two scalar functions sufficiently smooth on as their matrix counterpart . He proves the following a priori estimate :\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 of , where is a constant depending on , , and other parameters but not depending on the moduli of continuity of the coefficients. The integrability exponents of the norms in are subject to the relations • for , • is an arbitrary positive number for , the first one of which answers positively to a conjecture proposed by . ==Selected works==

Papers • , translated as . • , translated as . • , translated in English as . • , translated in English as . • Books • , translated in English as . • . A definitive monograph, giving a detailed study of a priori estimates of constant coefficient matrix differential operators defined on , with : translated as . • (also available with ). • . • (also available as ). • . • . • . There are also two revised and expanded editions: the French translation , and the (further revised and expanded) Russian translation . • . • . • . • . • . • . • . • . • . • . • . • . • . • (also published with ). First Russian edition published as . • ==See also==