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Regularity of stable solutions to semilinear elliptic equations

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hdl:2117/177176

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Cabré Vilagut, XavierMés informacióMés informacióMés informació
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Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
Document typeAudiovisual
Defense date2019-11-21
Rights accessOpen Access
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder
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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