A mass transportation approach for Sobolev inequalities in variable exponent spaces

In this paper we provide a proof of the Sobolev–Poincaré inequality for variable exponent spaces by means of mass transportation methods, in the spirit of Cordero-Erausquin et al. (Adv Math 182(2):307–332, 2004). The importance of this approach is that the method is flexible enough to deal with diff...

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Autores principales: Borthagaray, J.P., Fernández Bonder, J., Silva, A.
Formato: JOUR
Materias:
46E35
49J40
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00252611_v151_n1-2_p133_Borthagaray
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00252611_v151_n1-2_p133_Borthagaray
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spelling todo:paper_00252611_v151_n1-2_p133_Borthagaray2023-10-03T14:35:37Z A mass transportation approach for Sobolev inequalities in variable exponent spaces Borthagaray, J.P. Fernández Bonder, J. Silva, A. 46E35 49J40 In this paper we provide a proof of the Sobolev–Poincaré inequality for variable exponent spaces by means of mass transportation methods, in the spirit of Cordero-Erausquin et al. (Adv Math 182(2):307–332, 2004). The importance of this approach is that the method is flexible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result of Fan (J Math Anal Appl 339(2):1395–1412, 2008) by obtaining an explicit dependence of the exponent in the constant. © 2016, Springer-Verlag Berlin Heidelberg. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00252611_v151_n1-2_p133_Borthagaray
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 46E35
49J40
spellingShingle 46E35
49J40
Borthagaray, J.P.
Fernández Bonder, J.
Silva, A.
A mass transportation approach for Sobolev inequalities in variable exponent spaces
topic_facet 46E35
49J40
description In this paper we provide a proof of the Sobolev–Poincaré inequality for variable exponent spaces by means of mass transportation methods, in the spirit of Cordero-Erausquin et al. (Adv Math 182(2):307–332, 2004). The importance of this approach is that the method is flexible enough to deal with different inequalities. As an application, we also deduce the Sobolev-trace inequality improving the result of Fan (J Math Anal Appl 339(2):1395–1412, 2008) by obtaining an explicit dependence of the exponent in the constant. © 2016, Springer-Verlag Berlin Heidelberg.
format JOUR
author Borthagaray, J.P.
Fernández Bonder, J.
Silva, A.
author_facet Borthagaray, J.P.
Fernández Bonder, J.
Silva, A.
author_sort Borthagaray, J.P.
title A mass transportation approach for Sobolev inequalities in variable exponent spaces
title_short A mass transportation approach for Sobolev inequalities in variable exponent spaces
title_full A mass transportation approach for Sobolev inequalities in variable exponent spaces
title_fullStr A mass transportation approach for Sobolev inequalities in variable exponent spaces
title_full_unstemmed A mass transportation approach for Sobolev inequalities in variable exponent spaces
title_sort mass transportation approach for sobolev inequalities in variable exponent spaces
url http://hdl.handle.net/20.500.12110/paper_00252611_v151_n1-2_p133_Borthagaray
work_keys_str_mv AT borthagarayjp amasstransportationapproachforsobolevinequalitiesinvariableexponentspaces
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AT silvaa amasstransportationapproachforsobolevinequalitiesinvariableexponentspaces
AT borthagarayjp masstransportationapproachforsobolevinequalitiesinvariableexponentspaces
AT fernandezbonderj masstransportationapproachforsobolevinequalitiesinvariableexponentspaces
AT silvaa masstransportationapproachforsobolevinequalitiesinvariableexponentspaces
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