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

In this paper, we study the critical Sobolev embeddings W1,p(.)(Ω)⊂Lp*(.)(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 w...

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Detalles Bibliográficos
Autores principales: Fernández Bonder, J., Saintier, N., Silva, A.
Formato: JOUR
Materias:
Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_0022247X_v442_n1_p189_FernandezBonder
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario:In this paper, we study the critical Sobolev embeddings W1,p(.)(Ω)⊂Lp*(.)(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. © 2016 Elsevier Inc.

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