Vladimir Gilelevich Maz'ya
Vladimir Maz'ya (Russian: Владимир Гилелевич Мазья) (born December 31, 1937) (the family name is sometimes transliterated as Mazya, Maz'ja or Mazja) is a leading Swedish mathematician. He systematically made fundamental contributions to a wide array of areas in mathematical analysis and in the theory of partial differential equations. His early achievements include: his work on Sobolev spaces, in particular the discovery of the equivalence between Sobolev and isoperimetric/isocapacitary inequalities (1960), his counterexamples related to Hilbert's 19th and Hilbert's 20th problem (1968), his solution to V. Arnol'd's problem for the oblique derivative boundary value problem (1970) and to 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, achieved a series of definitive results in the spectral theory of the Schrödinger operator, 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 substantially 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.