Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms

This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are Pólya-Szegó type inequalities for these rearrangements. We also deal with the...

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Detalles Bibliográficos
Autores: Csató, Gyula, Mas Blesa, Albert
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2025
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:2445/227054
Acceso en línea:https://hdl.handle.net/2445/227054
Access Level:acceso abierto
Palabra clave:Equacions en derivades parcials
Desigualtats (Matemàtica)
Partial differential equations
Inequalities (Mathematics)
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spelling Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-normsCsató, GyulaMas Blesa, AlbertEquacions en derivades parcialsDesigualtats (Matemàtica)Partial differential equationsInequalities (Mathematics)This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are Pólya-Szegó type inequalities for these rearrangements. We also deal with the cases of equality. Our method uses, among others, some classical nonexpansivity results for rearrangements for which we provide some slight improvements. Our proof is based on the ideas of [Frank and Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct. Anal., 2008], where a new proof to deal with the cases of equality in the nonexpansivity theorem was given, albeit in a special case involving the rearrangement of only one function.American Mathematical Society (AMS)2026202620252026info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersion33 p.application/pdfhttps://hdl.handle.net/2445/227054Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)InglésVersió postprint del document publicat a: https://doi.org/10.1090/tran/9510Transactions of the American Mathematical Society, 2025, vol. 378, p. 7163-7197https://doi.org/10.1090/tran/9510cc-by-nc-nd (c) American Mathematical Society (AMS), 2025http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:recercat.cat:2445/2270542026-05-29T05:05:01Z
dc.title.none.fl_str_mv Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
title Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
spellingShingle Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
Csató, Gyula
Equacions en derivades parcials
Desigualtats (Matemàtica)
Partial differential equations
Inequalities (Mathematics)
title_short Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
title_full Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
title_fullStr Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
title_full_unstemmed Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
title_sort Strict rearrangement inequalities: nonexpansivity and periodic Gagliardo semi-norms
dc.creator.none.fl_str_mv Csató, Gyula
Mas Blesa, Albert
author Csató, Gyula
author_facet Csató, Gyula
Mas Blesa, Albert
author_role author
author2 Mas Blesa, Albert
author2_role author
dc.subject.none.fl_str_mv Equacions en derivades parcials
Desigualtats (Matemàtica)
Partial differential equations
Inequalities (Mathematics)
topic Equacions en derivades parcials
Desigualtats (Matemàtica)
Partial differential equations
Inequalities (Mathematics)
description This paper deals with the behavior of the periodic Gagliardo seminorm under two types of rearrangements, namely under a periodic, and respectively a cylindrical, symmetric decreasing rearrangement. Our two main results are Pólya-Szegó type inequalities for these rearrangements. We also deal with the cases of equality. Our method uses, among others, some classical nonexpansivity results for rearrangements for which we provide some slight improvements. Our proof is based on the ideas of [Frank and Seiringer, Non-linear ground state representations and sharp Hardy inequalities, J. Funct. Anal., 2008], where a new proof to deal with the cases of equality in the nonexpansivity theorem was given, albeit in a special case involving the rearrangement of only one function.
publishDate 2025
dc.date.none.fl_str_mv 2025
2026
2026
2026
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/227054
url https://hdl.handle.net/2445/227054
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Versió postprint del document publicat a: https://doi.org/10.1090/tran/9510
Transactions of the American Mathematical Society, 2025, vol. 378, p. 7163-7197
https://doi.org/10.1090/tran/9510
dc.rights.none.fl_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2025
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv cc-by-nc-nd (c) American Mathematical Society (AMS), 2025
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 33 p.
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society (AMS)
publisher.none.fl_str_mv American Mathematical Society (AMS)
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,811543

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