Existence of solution to a critical trace equation with variable exponent
Analysis of PDEs
2013-01-15 v1
Abstract
In this paper we study sufficient local conditions for the existence of non-trivial solution to a critical equation for the 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.
Cite
@article{arxiv.1301.2962,
title = {Existence of solution to a critical trace equation with variable exponent},
author = {Julian Fernandez Bonder and Nicolas Saintier and Analia Silva},
journal= {arXiv preprint arXiv:1301.2962},
year = {2013}
}
Comments
23 pages, submitted