English

A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces

Analysis of PDEs 2013-10-23 v2

Abstract

In this paper, we study the critical Sobolev embeddings W1,p(x)(Ω)Lp(x)(Ω)W^{1,p(x)}(\Omega)\subset L^{p^*(x)}(\Omega) for variable exponent Sobolev spaces from the point of view of the Γ\Gamma-convergence. More precisely we determine the Γ\Gamma-limit of subcritical approximation of the best constant associated with this embedding. As an application we provide a sufficient condition for the existence of extremals for the best constant.

Keywords

Cite

@article{arxiv.1310.4800,
  title  = {A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces},
  author = {Julián Fernández Bonder and Nicolas Saintier and Analia Silva},
  journal= {arXiv preprint arXiv:1310.4800},
  year   = {2013}
}
R2 v1 2026-06-22T01:49:07.974Z