Luis Caffarelli

Luis Angel Caffarelli (born December 8, 1948 in Buenos Aires ) is an American-Argentine mathematician who deals with partial differential equations .

Life

Caffarelli studied at the University of Buenos Aires , where he received his master's degree in 1968 and his doctorate in 1972 with Calixto Calderón. He then went to the University of Minnesota, where he was Assistant Professor in 1975, Associate Professor in 1977 and Professor from 1979 to 1983. At the same time he was a professor at the Courant Institute of Mathematical Sciences of New York University from 1980 to 1982 . From 1983 to 1986 he was a professor at the University of Chicago and from 1986 to 1996 at the Institute for Advanced Study . From 1994 to 1997 he was again a professor at the Courant Institute, and since 1997 he has been a professor at the University of Texas at Austin (Department of Computational Engineering and Sciences).

Caffarelli was particularly concerned with free boundary value problems of nonlinear partial differential equations . The edges, on which the boundary conditions for the solution of the differential equation problem are given, are variable (an example is the description of the freezing of a lake with partial differential equations). He is also known for his investigations into special non-linear partial differential equations, such as the Monge-Ampère equation (together with Louis Nirenberg , Joel Spruck and Joseph Kohn ) or partial differential equations for flows in porous media (important and examined at great expense in the Oil production). In 1990 he introduced viscosity solutions for this purpose . In 1982, with Nirenberg and Robert V. Kohn , he proved regularity theorems about the solution of the Navier-Stokes equations ( theorem of Caffarelli-Kohn-Nirenberg ).

In 2002, together with Michail Feldman and Robert McCann, he gave constructive proof of a transport problem by Monge , which V. Sudakov first solved in 1976.

Caffarelli has both Argentine and US citizenship. He is a member of the American Academy of Arts and Sciences (since 1986), the National Academy of Sciences (since 1991), the Papal and Argentine Academy of Sciences and the Accademia dei Lincei. He is a fellow of the American Mathematical Society . Caffarelli holds honorary doctorates from the Universities of Madrid, San Luis, La Plata and the École normal supérieure . In 1982 he received the Stampacchia Prize and in 1984 the Bôcher Memorial Prize . In 1985 he was a Guggenheim Fellow. He was invited speaker at the International Congress of Mathematicians in Warsaw in 1983 (Variational problems with free boundaries) and in Beijing in 2002 (Plenary lecture: Nonlinear elliptic theory and the Monge-Ampere-Equation ). In 2005 he received the Rolf Schock Prize , in 2009 he was awarded the Leroy P. Steele Prize for Lifetime Achievement and in 2014 the Seminal Contribution to Research Prize for his work with Nirenberg and Kohn in 1982. In 2012 he received the Wolf Prize. Prize in Mathematics and the Shaw Prize in Mathematics in 2018 .

Ovidiu Savin is one of his doctoral students .

Fonts

• with Cabré: Fully Nonlinear Elliptic Equations. American Mathematical Society, 1995, ISBN 0-8218-0437-5 .
• with Salsa: Geometric Approach to Free Boundary Problems. American Mathematical Society, 2005, ISBN 0-8218-3784-2 .

Web links

• Homepage of Caffarelli at the University of Texas
• At the shock price for Caffarelli

Individual evidence

1. ↑ Caffarelli, Kohn, Nirenberg Partial regularity of suitable weak solutions of the Navier-Stokes equations , Communications Pure and Applied Mathematics, Volume 35, 1982, pp. 771-831
2. ↑ Luis Caffarelli in the Mathematics Genealogy Project (English)