The peak of the solution of elliptic equations

2015/11/15 by Nee, Janpou
#35J57 #35J61 (Primary) #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.04644

Abstract

A counter example of inheritance of convexity of domain of positive solution of Dirichlet boundary value problem and the hot spot problem that proposed by J. Rauch is given. The difficulty of these two problems is that the critical points of the solutions is not singleton but a level curve. However, using Pohozeav identity locally, partial answer to both problems can be derived.

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