Analysis Seminar

Stable solutions to semilinear elliptic equations are smooth up to dimension 9

Speaker: Xavier Cabre, ICREA and UPC (Barcelona)

Location: Warren Weaver Hall 1302

Date: Thursday, October 3, 2019, 11 a.m.


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 this talk I will describe a recent
work with Figalli, Ros-Oton, and Serra, where we prove that stable
solutions are smooth up to the optimal dimension 9. This answers also to
a famous open problem posed by Brezis concerning the regularity of
extremal solutions to Gelfand-type problems.