Analysis Seminar

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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.

Synopsis:

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.