Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10316/44406 https://doi.org/10.1093/imrn/rnx068 |
Resumo: | A longstanding conjecture in elliptic regularity theory inquires whether a W^{1,p} function whose p-laplacian is bounded is locally of class C^{1,\frac{1}{p-1}}. While it is well known that such functions are of class C^{1,\alpha} for some unknown 0 < α < 1, establishing the sharp estimate turns out to be a rather delicate problem. Quite recently, the authors managed to establish the conjecture in the plane. In this article, we address the conjecture in higher dimensions and confirm its validity in a number of other meaningful cases. |
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Towards the $C^{p^\prime}$-Regularity Conjecture in Higher DimensionsA longstanding conjecture in elliptic regularity theory inquires whether a W^{1,p} function whose p-laplacian is bounded is locally of class C^{1,\frac{1}{p-1}}. While it is well known that such functions are of class C^{1,\alpha} for some unknown 0 < α < 1, establishing the sharp estimate turns out to be a rather delicate problem. Quite recently, the authors managed to establish the conjecture in the plane. In this article, we address the conjecture in higher dimensions and confirm its validity in a number of other meaningful cases.Oxford University Press2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44406http://hdl.handle.net/10316/44406https://doi.org/10.1093/imrn/rnx068https://doi.org/10.1093/imrn/rnx068enghttps://doi.org/10.1093/imrn/rnx068Araújo, Damião J.Teixeira, Eduardo V.Urbano, José Miguelinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2021-06-29T10:03:14Zoai:estudogeral.uc.pt:10316/44406Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:23.058119Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
title |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
spellingShingle |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions Araújo, Damião J. |
title_short |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
title_full |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
title_fullStr |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
title_full_unstemmed |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
title_sort |
Towards the $C^{p^\prime}$-Regularity Conjecture in Higher Dimensions |
author |
Araújo, Damião J. |
author_facet |
Araújo, Damião J. Teixeira, Eduardo V. Urbano, José Miguel |
author_role |
author |
author2 |
Teixeira, Eduardo V. Urbano, José Miguel |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Araújo, Damião J. Teixeira, Eduardo V. Urbano, José Miguel |
description |
A longstanding conjecture in elliptic regularity theory inquires whether a W^{1,p} function whose p-laplacian is bounded is locally of class C^{1,\frac{1}{p-1}}. While it is well known that such functions are of class C^{1,\alpha} for some unknown 0 < α < 1, establishing the sharp estimate turns out to be a rather delicate problem. Quite recently, the authors managed to establish the conjecture in the plane. In this article, we address the conjecture in higher dimensions and confirm its validity in a number of other meaningful cases. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10316/44406 http://hdl.handle.net/10316/44406 https://doi.org/10.1093/imrn/rnx068 https://doi.org/10.1093/imrn/rnx068 |
url |
http://hdl.handle.net/10316/44406 https://doi.org/10.1093/imrn/rnx068 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://doi.org/10.1093/imrn/rnx068 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Oxford University Press |
publisher.none.fl_str_mv |
Oxford University Press |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799133820717367296 |