Conductor Sobolev-type estimates and isocapacitary inequalities

In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and s...

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Autores: Cerdà Martín, Joan Lluís, Martín i Pedret, Joaquim|||0000-0002-7467-787X, Silvestre, Pilar
Formato: artículo
Fecha de publicación:2012
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:115176
Acesso em linha:https://ddd.uab.cat/record/115176
https://dx.doi.org/urn:doi:10.1512/iumj.2012.61.4709
Access Level:acceso abierto
Palavra-chave:Convexity
Lower estimates
Sobolev spaces
Rearrangement invariant spaces
Sobolev-type inequalities
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spelling Conductor Sobolev-type estimates and isocapacitary inequalitiesCerdà Martín, Joan LluísMartín i Pedret, Joaquim|||0000-0002-7467-787XSilvestre, PilarConvexityLower estimatesSobolev spacesRearrangement invariant spacesSobolev-type inequalitiesIn this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions. 22012-01-0120122012-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/115176https://dx.doi.org/urn:doi:10.1512/iumj.2012.61.4709reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:1151762026-06-06T12:50:31Z
dc.title.none.fl_str_mv Conductor Sobolev-type estimates and isocapacitary inequalities
title Conductor Sobolev-type estimates and isocapacitary inequalities
spellingShingle Conductor Sobolev-type estimates and isocapacitary inequalities
Cerdà Martín, Joan Lluís
Convexity
Lower estimates
Sobolev spaces
Rearrangement invariant spaces
Sobolev-type inequalities
title_short Conductor Sobolev-type estimates and isocapacitary inequalities
title_full Conductor Sobolev-type estimates and isocapacitary inequalities
title_fullStr Conductor Sobolev-type estimates and isocapacitary inequalities
title_full_unstemmed Conductor Sobolev-type estimates and isocapacitary inequalities
title_sort Conductor Sobolev-type estimates and isocapacitary inequalities
dc.creator.none.fl_str_mv Cerdà Martín, Joan Lluís
Martín i Pedret, Joaquim|||0000-0002-7467-787X
Silvestre, Pilar
author Cerdà Martín, Joan Lluís
author_facet Cerdà Martín, Joan Lluís
Martín i Pedret, Joaquim|||0000-0002-7467-787X
Silvestre, Pilar
author_role author
author2 Martín i Pedret, Joaquim|||0000-0002-7467-787X
Silvestre, Pilar
author2_role author
author
dc.subject.none.fl_str_mv Convexity
Lower estimates
Sobolev spaces
Rearrangement invariant spaces
Sobolev-type inequalities
topic Convexity
Lower estimates
Sobolev spaces
Rearrangement invariant spaces
Sobolev-type inequalities
description In this paper we present an integral inequality connecting a function space (quasi-)norm of the gradient of a function to an integral of the corresponding capacity of the conductor between two level surfaces of the function, which extends the estimates obtained by V. Maz'ya and S. Costea, and sharp capacitary inequalities due to V. Maz'ya in the case of the Sobolev norm. The inequality, obtained under appropriate convexity conditions on the function space, gives a characterization of Sobolev-type inequalities involving two measures, necessary and sufficient conditions for Sobolev isocapacitary-type inequalities, and self-improvements for integrability of Lipschitz functions.
publishDate 2012
dc.date.none.fl_str_mv 2
2012-01-01
2012
2012-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/115176
https://dx.doi.org/urn:doi:10.1512/iumj.2012.61.4709
url https://ddd.uab.cat/record/115176
https://dx.doi.org/urn:doi:10.1512/iumj.2012.61.4709
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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