Stable solutions to semilinear elliptic equations

Speaker:  Alessio Figalli - ETH Zurich
  Friday, November 27, 2020 at 2:30 PM
Stable solutions to semilinear elliptic PDEs appear in several
problems. It is known since the 1970’s that, in dimension n > 9, there
exist singular stable solutions. In this talk I will describe a recent work
with Cabré, Ros-Oton, and Serra, where we prove that stable solutions in
dimension n ≤ 9 are smooth. This answers also a famous open problem posed
by Brezis, concerning the regularity of extremal solutions to the Gelfand

Programme Director
Marco Caliari

Publication date
November 17, 2020