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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Autores principales: Fernandez Bonder, Julian, Silva, Analia Concepcion
Publicado: 2016
Materias:
Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v442_n1_p189_FernandezBonder
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
id paper:paper_0022247X_v442_n1_p189_FernandezBonder
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spelling paper:paper_0022247X_v442_n1_p189_FernandezBonder2023-06-08T14:48:00Z A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces Fernandez Bonder, Julian Silva, Analia Concepcion Concentration compactness Critical exponents Sobolev embedding Variable exponents 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. Fil:Fernández Bonder, J. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Silva, A. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v442_n1_p189_FernandezBonder http://hdl.handle.net/20.500.12110/paper_0022247X_v442_n1_p189_FernandezBonder
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
spellingShingle Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
Fernandez Bonder, Julian
Silva, Analia Concepcion
A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
topic_facet Concentration compactness
Critical exponents
Sobolev embedding
Variable exponents
description 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.
author Fernandez Bonder, Julian
Silva, Analia Concepcion
author_facet Fernandez Bonder, Julian
Silva, Analia Concepcion
author_sort Fernandez Bonder, Julian
title A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
title_short A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
title_full A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
title_fullStr A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
title_full_unstemmed A Gamma convergence approach to the critical Sobolev embedding in variable exponent spaces
title_sort gamma convergence approach to the critical sobolev embedding in variable exponent spaces
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v442_n1_p189_FernandezBonder
http://hdl.handle.net/20.500.12110/paper_0022247X_v442_n1_p189_FernandezBonder
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AT silvaanaliaconcepcion agammaconvergenceapproachtothecriticalsobolevembeddinginvariableexponentspaces
AT fernandezbonderjulian gammaconvergenceapproachtothecriticalsobolevembeddinginvariableexponentspaces
AT silvaanaliaconcepcion gammaconvergenceapproachtothecriticalsobolevembeddinginvariableexponentspaces
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