Ovidiu Savin | |
|---|---|
 Savin in 2003 | |
| Born | 1 January 1977 |
| Nationality | Romanian |
| Alma mater | University of Texas at Austin |
| Awards | Stampacchia Medal (2012) |
| Scientific career | |
| Fields | Mathematics |
| Institutions | Columbia University |
| Doctoral advisor | Luis Caffarelli |
Ovidiu Vasile Savin (born January 1, 1977) is a Romanian-American mathematician who is active in the field of the partial differential equations.
Savin received his Ph.D. in mathematics from the University of Texas at Austin in 2003 having Luis Caffarelli as advisor; he is professor of mathematics at Columbia University. Savin is mostly known for his important work on Ennio De Giorgi's conjecture about global solutions to certain semilinear equations, that he proved up to dimension 8. [1] It is to be noticed that the conjecture turns out to be false in higher dimensions, as eventually proved by Manuel del Pino, Michał Kowalczyk, and Juncheng Wei. [2] Savin has also worked on various regularity questions proving the gradient continuity of solutions to the infinity-Laplacian equation in two dimensions and obtaining results on the boundary regularity of solutions to the Monge–Ampère equation.
Savin won a gold medal with a perfect score in the 1995 International Mathematical Olympiad. [3] As an undergraduate at the University of Pittsburgh in 1997, Savin was a William Lowell Putnam Mathematical Competition fellow. [4] Savin was an invited speaker at the International Congress of Mathematicians in 2006. [5] He was awarded the Stampacchia Medal in 2012.
John Forbes Nash, Jr., known and published as John Nash, was an American mathematician who made fundamental contributions to game theory, real algebraic geometry, differential geometry, and partial differential equations. Nash and fellow game theorists John Harsanyi and Reinhard Selten were awarded the 1994 Nobel Memorial Prize in Economics. In 2015, he and Louis Nirenberg were awarded the Abel Prize for their contributions to the field of partial differential equations.
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Ennio De Giorgi was an Italian mathematician who worked on partial differential equations and the foundations of mathematics.
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Hilbert's nineteenth problem is one of the 23 Hilbert problems, set out in a list compiled by David Hilbert in 1900. It asks whether the solutions of regular problems in the calculus of variations are always analytic. Informally, and perhaps less directly, since Hilbert's concept of a "regular variational problem" identifies this precisely as a variational problem whose Euler–Lagrange equation is an elliptic partial differential equation with analytic coefficients, Hilbert's nineteenth problem, despite its seemingly technical statement, simply asks whether, in this class of partial differential equations, any solution inherits the relatively simple and well understood property of being an analytic function from the equation it satisfies. Hilbert's nineteenth problem was solved independently in the late 1950s by Ennio De Giorgi and John Forbes Nash, Jr.
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