Boundedness of stable solutions to semilinear elliptic equations: a survey

2017/04/20 by Cabre, Xavier
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.06063

Abstract

This article is a survey on boundedness results for stable solutions to semilinear elliptic problems. For these solutions, we present the currently known L^∞ 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.

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