Stable solutions to semilinear elliptic equations

Alessio Figalli (ETH Zurich)

05-Nov-2020, 14:00-14:50 (3 years ago)

Abstract: 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 Cabr\'e, 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 problem.

analysis of PDEs

Audience: researchers in the topic

( paper )


PDE seminar via Zoom

Organizer: Quoc-Hung Nguyen*
*contact for this listing

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