Louis Nirenberg was a Canadian-American mathematician, considered one of the most outstanding mathematicians of the 20th century.
Luis Ángel Caffarelli is an Argentine-American mathematician. He studies partial differential equations and their applications. Caffarelli is a professor of mathematics at the University of Texas at Austin, and the winner of the 2023 Abel Prize.
Lawrence Craig Evans is an American mathematician and Professor of Mathematics at the University of California, Berkeley.
Aleksei Vasilyevich Pogorelov, was a Soviet mathematician. Specialist in the field of convex and differential geometry, geometric PDEs and elastic shells theory, the author of novel school textbooks on geometry and university textbooks on analytical geometry, on differential geometry, and on the foundations of geometry.
In mathematics, a (real) Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u of two variables x,y is of Monge–Ampère type if it is linear in the determinant of the Hessian matrix of u and in the second-order partial derivatives of u. The independent variables (x,y) vary over a given domain D of R2. The term also applies to analogous equations with n independent variables. The most complete results so far have been obtained when the equation is elliptic.
Cédric Patrice Thierry Villani is a French politician and mathematician working primarily on partial differential equations, Riemannian geometry and mathematical physics. He was awarded the Fields Medal in 2010, and he was the director of Sorbonne University's Institut Henri Poincaré from 2009 to 2017. As of September 2022, he is a professor at Institut des Hautes Études Scientifiques.
Erhard Heinz was a German mathematician known for his work on partial differential equations, in particular the Monge–Ampère equation. He worked as professor in Stanford, Munich and from 1966 until his retirement 1992 at the University of Göttingen.
Maciej Zworski is a Polish-Canadian mathematician, currently a professor of mathematics at the University of California, Berkeley. His mathematical interests include microlocal analysis, scattering theory, and partial differential equations.
In mathematics, k-Hessian equations are partial differential equations (PDEs) based on the Hessian matrix. More specifically, a Hessian equation is the k-trace, or the kth elementary symmetric polynomial of eigenvalues of the Hessian matrix. When k ≥ 2, the k-Hessian equation is a fully nonlinear partial differential equation. It can be written as , where , , and , are the eigenvalues of the Hessian matrix and , is a th elementary symmetric polynomial.
Alessio Figalli is an Italian mathematician working primarily on calculus of variations and partial differential equations.
Ovidiu Vasile Savin is a Romanian-American mathematician who is active in the field of the partial differential equations.
J. (Jean) François Treves is an American mathematician, specializing in partial differential equations.
Robert Miller Hardt is an American mathematician. His research deals with geometric measure theory, partial differential equations, and continuum mechanics. He is particularly known for his work with Leon Simon proving the boundary regularity of volume minimizing hypersurfaces.
Duong Hong Phong is an American mathematician of Vietnamese origin. He is a professor of mathematics at Columbia University. He is known for his research on complex analysis, partial differential equations, string theory and complex geometry.
Gábor Székelyhidi is a Hungarian mathematician, specializing in differential geometry.
Guy David is a French mathematician, specializing in analysis.
Sébastien Boucksom is a French mathematician.
Xavier Ros Oton is a Spanish mathematician who works on partial differential equations (PDEs). He is an ICREA Research Professor and a Full Professor at the University of Barcelona.
In mathematics, the Suita conjecture is a conjecture related to the theory of the Riemann surface, the boundary behavior of conformal maps, the theory of Bergman kernel, and the theory of the L2 extension. The conjecture states the following:
Suita (1972): Let R be an Riemann surface, which admits a nontrivial Green function . Let be a local coordinate on a neighborhood of satisfying . Let be the Bergman kernel for holomorphic (1, 0) forms on R. We define , and . Let be the logarithmic capacity which is locally defined by on R. Then, the inequality holds on the every open Riemann surface R, and also, with equality, then or, R is conformally equivalent to the unit disc less a (possible) closed set of inner capacity zero.
Valentino Tosatti is an Italian mathematician.
