Existence of solution to a critical trace equation with variable exponent

2013/01/14 by Bonder, Julian Fernandez, Saintier, Nicolas, Silva, Analia
#35B33 #35J92 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1301.2962

Abstract

In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the p(x)-Laplacian where the critical term is placed as a source through the boundary of the domain. The proof relies on a suitable generalization of the concentration--compactness principle for the trace embedding for variable exponent Sobolev spaces and the classical mountain pass theorem.

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