Luis Caffarelli

Luis Caffarelli is one of the most influential mathematicians of our time, who made fundamental contributions to the theory of partial differential equations, especially to the study of regularity of solutions. In the context of the Navier–Stokes problem, his key 1982 work, written jointly with Robert Kohn and Louis Nirenberg, established partial regularity of suitable weak solutions: the set of possible singularities has one-dimensional Hausdorff measure equal to zero. This means that singularities, if they occur, are localized in a very small set, which became an important step in understanding possible blow-up of solutions. Caffarelli also developed the theory of free boundaries and regularity of nonlinear elliptic and parabolic equations, for which he was awarded the Abel Prize in 2023.

Biography

Luis Caffarelli was born in Buenos Aires, Argentina, in 1948. He received his PhD from the University of Buenos Aires in 1972 under the supervision of Calixto Calderón. He worked at the University of Minnesota, the University of Chicago, the Courant Institute, Princeton University, and the University of Texas at Austin. Among his awards are the Bôcher Prize (1984), the Wolf Prize (2012), the Shaw Prize (2018), and the Abel Prize (2023).

Key discoveries

Together with Kohn and Nirenberg, proved partial regularity of suitable weak solutions of the Navier–Stokes equations: the set of singular points has zero one-dimensional Hausdorff measure (1982).
Developed regularity theory for free boundary problems, including the Stefan problem and the obstacle problem.
Contributed to the theory of nonlinear elliptic equations, in particular to the regularity of solutions of Monge–Ampère equations.

Biography

Key discoveries

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