A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2017 |
| Outros Autores: | , |
| Tipo de documento: | Artigo |
| Idioma: | eng |
| Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
| DOI: | 10.1016/j.aim.2017.06.027 |
| 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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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 A proof of the C^p'-regularity conjecture in the plane p ′ -regularity conjecture in the plane Araújo, Damião J. 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 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 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. Araújo, Damião J. Teixeira, Eduardo V. Urbano, José Miguel 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 |
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Elsevier |
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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 |
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RCAAP |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1822183422824546304 |
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10.1016/j.aim.2017.06.027 |