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arXiv · 1310.4800

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

Julián Fernández Bonder·Nicolas Saintier·Analia Silva
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Abstract

In this paper, we study the critical Sobolev embeddings $W^{1,p(x)}(Ω)\subset L^{p^*(x)}(Ω)$ for variable exponent Sobolev spaces from the point of view of the $Γ$-convergence. More precisely we determine the $Γ$-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.

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Julián Fernández Bonder, Nicolas Saintier, Analia Silva. 2013-10-22. A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces. https://arxiv.org/abs/1310.4800

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