Regularity of stable solutions to semilinear elliptic equations

Cabré Vilagut, Xavier

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Cabré Vilagut, Xavier

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Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística

Document typeAudiovisual

Defense date2019-11-21

Rights accessOpen Access

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Abstract

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.

SubjectsDifferential equations, Partial, Equacions en derivades parcials

Is part ofWorkshop in honor of Alessio Figalli's "Doctor Honoris Causa at UPC" (21-novembre-2019)

URIhttp://hdl.handle.net/2117/177176

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