Regularity of stable solutions

to semilinear elliptic equations

up to dimension 9

A mini course by

Xavier Cabré

(ICREA and Universitat Politècnica de Catalunya)

November 29 - November 30, 2023

Universidad Autónoma de Madrid

Departamento de Matemáticas

Aula 520 (módulo 17)

PhD in Mathematics, Courant Institute, advisor Louis Nirenberg, 1994. Kurt Friedrichs Prize, 1995. Member of the Institute for Advanced Study, Princeton, 1994-95. Habilitation à diriger des recherches, Université Paris VI, 1998. Harrington Faculty Fellow and Tenure Associate Professor, The University of Texas at Austin, 2001-03. ICREA Research Professor at the Universitat Politècnica de Catalunya, since 2003. Fellow of the American Mathematical Society, inaugural class, 2013. Plenary speaker at the 8th European Congress of Mathematics, 2021. Frontiers of Science Award, The first International Congress of Basic Science, Beijing 2023.

Abstract: The regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970's. It was initiated by a work of Crandall and Rabinowitz, motivated by the Gelfand problem in combustion theory. The theory experienced a revival in the mid-nineties after new progress made by Brezis and collaborators. I will present these developments and my work in collaboration with Figalli, Ros-Oton, and Serra, which finally establishes the regularity of stable solutions up to the optimal dimension 9. I will also describe a more recent paper of mine which provides full quantitative proofs of the regularity results. I will finally comment on similar progress and open problems for related equations.

Schedule

Lecture 1: November 29th, 11:00 - 12:30.

Lecture 2: November 30th, 11:00 - 12:30.

Lecture 3: November 30th, 16:00 - 17:30.

No registration is needed and everybody is welcome to attend

Page updated

Google Sites

Report abuse