Workshop: Regularity of stable solutions to semilinear elliptic equations up to dimension 9

Date: 2022-09-06

Time: 10:00 - 11:00

Zoom link:


Xavier Cabré‪


The regularity of stable solutions to semilinear elliptic PDEs has been studied since the 1970’s. In dimensions 10 and higher, there exist singular stable energy solutions. In these talks I will describe a recent work in collaboration with Figalli, Ros-Oton, and Serra, where we prove that stable solutions are smooth up to the optimal dimension 9. This answers to an open problem posed by Brezis in the mid-nineties concerning the regularity of extremal solutions to Gelfand-type problems.