On the Sobolev embedding theorem for variable exponent spaces in the critical range

In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration-Compactness Theorem fo...

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Autores principales:	Fernandez Bonder, Julian, Silva, Analia Concepcion
Publicado:	2012
Materias:	Concentration compactness Critical exponents Sobolev embedding Variable exponents
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v253_n5_p1604_FernandezBonder http://hdl.handle.net/20.500.12110/paper_00220396_v253_n5_p1604_FernandezBonder
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00220396_v253_n5_p1604_FernandezBonder
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spelling	paper:paper_00220396_v253_n5_p1604_FernandezBonder2023-06-08T14:45:12Z On the Sobolev embedding theorem for variable exponent spaces in the critical range Fernandez Bonder, Julian Silva, Analia Concepcion Concentration compactness Critical exponents Sobolev embedding Variable exponents In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration-Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico. © 2012 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. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v253_n5_p1604_FernandezBonder http://hdl.handle.net/20.500.12110/paper_00220396_v253_n5_p1604_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 On the Sobolev embedding theorem for variable exponent spaces in the critical range
topic_facet	Concentration compactness Critical exponents Sobolev embedding Variable exponents
description	In this paper we study the Sobolev embedding theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. The proof is based on a suitable refinement of the estimates in the Concentration-Compactness Theorem for variable exponents and an adaptation of a convexity argument due to P.L. Lions, F. Pacella and M. Tricarico. © 2012 Elsevier Inc..
author	Fernandez Bonder, Julian Silva, Analia Concepcion
author_facet	Fernandez Bonder, Julian Silva, Analia Concepcion
author_sort	Fernandez Bonder, Julian
title	On the Sobolev embedding theorem for variable exponent spaces in the critical range
title_short	On the Sobolev embedding theorem for variable exponent spaces in the critical range
title_full	On the Sobolev embedding theorem for variable exponent spaces in the critical range
title_fullStr	On the Sobolev embedding theorem for variable exponent spaces in the critical range
title_full_unstemmed	On the Sobolev embedding theorem for variable exponent spaces in the critical range
title_sort	on the sobolev embedding theorem for variable exponent spaces in the critical range
publishDate	2012
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00220396_v253_n5_p1604_FernandezBonder http://hdl.handle.net/20.500.12110/paper_00220396_v253_n5_p1604_FernandezBonder
work_keys_str_mv	AT fernandezbonderjulian onthesobolevembeddingtheoremforvariableexponentspacesinthecriticalrange AT silvaanaliaconcepcion onthesobolevembeddingtheoremforvariableexponentspacesinthecriticalrange
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On the Sobolev embedding theorem for variable exponent spaces in the critical range

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