On the Sobolev embedding theorem for variable exponent spaces in the critical range
Analysis of PDEs
2012-11-06 v1 Functional Analysis
Abstract
In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration--Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico.
Cite
@article{arxiv.1111.6952,
title = {On the Sobolev embedding theorem for variable exponent spaces in the critical range},
author = {Julian Fernandez Bonder and Nicolas Saintier and Analia Silva},
journal= {arXiv preprint arXiv:1111.6952},
year = {2012}
}
Comments
15 pages, submitted