Regularity of stable solutions to semilinear elliptic equations
Chair / Department / Institute
Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
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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 to a famous open problem posed by Brezis in the mid-nineties concerning the regularity of extremal solutions to Gelfand-type problems.
Is part ofWorkshop in honor of Alessio Figalli's "Doctor Honoris Causa at UPC" (21-novembre-2019)