A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane

Detalhes bibliográficos
Autor(a) principal: Araújo, Damião J.
Data de Publicação: 2017
Outros Autores: Teixeira, Eduardo V., Urbano, José Miguel
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10316/44401
https://doi.org/10.1016/j.aim.2017.06.027
Resumo: We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^p'=C^(1,1/(p-1)) ; this regularity is optimal.
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spelling A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the planeWe establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^p'=C^(1,1/(p-1)) ; this regularity is optimal.Elsevier2017info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://hdl.handle.net/10316/44401http://hdl.handle.net/10316/44401https://doi.org/10.1016/j.aim.2017.06.027https://doi.org/10.1016/j.aim.2017.06.027enghttps://doi.org/10.1016/j.aim.2017.06.027Araújo, 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:RCAAP2021-06-29T10:02:56Zoai:estudogeral.uc.pt:10316/44401Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:53:22.850053Repositório 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 A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
title A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
spellingShingle A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
Araújo, Damião J.
title_short A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
title_full A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
title_fullStr A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
title_full_unstemmed A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
title_sort A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
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 We establish a new oscillation estimate for solutions of nonlinear partial differential equations of elliptic, degenerate type. This new tool yields a precise control on the growth rate of solutions near their set of critical points, where ellipticity degenerates. As a consequence, we are able to prove the planar counterpart of the longstanding conjecture that solutions of the degenerate p-Poisson equation with a bounded source are locally of class C^p'=C^(1,1/(p-1)) ; this regularity is optimal.
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/10316/44401
http://hdl.handle.net/10316/44401
https://doi.org/10.1016/j.aim.2017.06.027
https://doi.org/10.1016/j.aim.2017.06.027
url http://hdl.handle.net/10316/44401
https://doi.org/10.1016/j.aim.2017.06.027
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://doi.org/10.1016/j.aim.2017.06.027
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
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
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instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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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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