Vladimir Gilelevich Maz'ya (Russian: Владимир Гилелевич Мазья; born 31 December 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] Mazya's 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 & Szőkefalvi-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.
In recent years, he proved a Wiener's type criterion for higher order elliptic equations, together with Mikhail 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.
[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.
[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.
[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.
[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.