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

2013/10/17 by Julián Fernández Bonder, Bonder, Julián Fernández, Nicolas Saintier +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1310.4800

openalex publication_date 2013/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the critical Sobolev embeddings\nW^1,p(x)(\Ω)\⊂ L^{p^*(x)}(\Ω) for variable exponent Sobolev\nspaces from the point of view of the \Γ-convergence. More precisely we\ndetermine the \Γ-limit of subcritical approximation of the best constant\nassociated with this embedding. As an application we provide a sufficient\ncondition for the existence of extremals for the best constant.\n

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