For his «seminal contributions to regularity theory for nonlinear partial differential equations including free-boundary problems and the Monge–Ampère equation»

The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2023 to Luis A. Caffarelli of the University of Texas at Austin, USA.

«Caffarelli’s theorems have radically changed our understanding of classes of nonlinear partial differential equations with wide applications. The results are technically virtuous, covering many different areas of mathematics and its applications,» says chair of the Abel Committee Helge Holden.

«A large part of Luis A. Caffarelli’s work concerns free-boundary problems. Consider, for instance, the problem of ice melting into water. Here the free boundary is the interface between water and ice; it is part of the unknown that is to be determined. Another example is provided by water seeping through a porous medium – again the interface of water and the medium is to be understood. Caffarelli has given penetrating solutions to these problems with applications to solid–liquid interfaces, jet and cavitational flows, and gas and liquid flows in porous media, as well as financial mathematics», is mentioned in the portal https://abelprize.no/