Boundedness of stable solutions to semilinear elliptic equations: A survey

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Title:	Boundedness of stable solutions to semilinear elliptic equations: A survey
Author:	Cabré Vilagut, Xavier
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. EDP - Equacions en Derivades Parcials i Aplicacions
Abstract:	This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L8 estimates that hold for all nonlinearities. Such estimates are known to hold up to dimension 4. They are expected to be true also in dimensions 5 to 9, but this is still an open problem which has only been established in the radial case.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Differential equations, Elliptic -Stable Solutions -Semilinear Elliptic Equations -Boundedness of Solutions -Equacions diferencials -Equacions diferencials el·líptiques -- Solucions numèriques
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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