On minima of a functional of the gradient: upper and lower solutions
Autor(a) principal: | |
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Data de Publicação: | 2006 |
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/10174/2548 |
Resumo: | This paper studies a scalar minimization problem with an integral functional of the gradient under affine boundary conditions. A new approach is proposed using a minimal and a maximal solution to the convexified problem. We prove a density result: any relaxed solution continuously depending on boundary data may be approximated uniformly by solutions of the nonconvex problem keeping continuity relative to data. We also consider solutions to the nonconvex problem having Lipschitz dependence on boundary data with the best Lipschitz constant. |
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On minima of a functional of the gradient: upper and lower solutionsscalar variational problemnonconvex lagrangianBaire category theoremcontinuous selectionrelaxationThis paper studies a scalar minimization problem with an integral functional of the gradient under affine boundary conditions. A new approach is proposed using a minimal and a maximal solution to the convexified problem. We prove a density result: any relaxed solution continuously depending on boundary data may be approximated uniformly by solutions of the nonconvex problem keeping continuity relative to data. We also consider solutions to the nonconvex problem having Lipschitz dependence on boundary data with the best Lipschitz constant.Elsevier Ltd.2011-02-10T10:00:50Z2011-02-102006-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article249292 bytesapplication/pdfhttp://hdl.handle.net/10174/2548http://hdl.handle.net/10174/2548eng1437-145964Nonlinear Analysislivregoncha@uevora.ptornelas@uevora.pt334Goncharov, VladimirOrnelas, Antónioinfo: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:RCAAP2024-01-03T18:39:05Zoai:dspace.uevora.pt:10174/2548Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:58:13.728512Repositório 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 |
On minima of a functional of the gradient: upper and lower solutions |
title |
On minima of a functional of the gradient: upper and lower solutions |
spellingShingle |
On minima of a functional of the gradient: upper and lower solutions Goncharov, Vladimir scalar variational problem nonconvex lagrangian Baire category theorem continuous selection relaxation |
title_short |
On minima of a functional of the gradient: upper and lower solutions |
title_full |
On minima of a functional of the gradient: upper and lower solutions |
title_fullStr |
On minima of a functional of the gradient: upper and lower solutions |
title_full_unstemmed |
On minima of a functional of the gradient: upper and lower solutions |
title_sort |
On minima of a functional of the gradient: upper and lower solutions |
author |
Goncharov, Vladimir |
author_facet |
Goncharov, Vladimir Ornelas, António |
author_role |
author |
author2 |
Ornelas, António |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Goncharov, Vladimir Ornelas, António |
dc.subject.por.fl_str_mv |
scalar variational problem nonconvex lagrangian Baire category theorem continuous selection relaxation |
topic |
scalar variational problem nonconvex lagrangian Baire category theorem continuous selection relaxation |
description |
This paper studies a scalar minimization problem with an integral functional of the gradient under affine boundary conditions. A new approach is proposed using a minimal and a maximal solution to the convexified problem. We prove a density result: any relaxed solution continuously depending on boundary data may be approximated uniformly by solutions of the nonconvex problem keeping continuity relative to data. We also consider solutions to the nonconvex problem having Lipschitz dependence on boundary data with the best Lipschitz constant. |
publishDate |
2006 |
dc.date.none.fl_str_mv |
2006-01-01T00:00:00Z 2011-02-10T10:00:50Z 2011-02-10 |
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/10174/2548 http://hdl.handle.net/10174/2548 |
url |
http://hdl.handle.net/10174/2548 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
1437-1459 64 Nonlinear Analysis livre goncha@uevora.pt ornelas@uevora.pt 334 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
249292 bytes application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier Ltd. |
publisher.none.fl_str_mv |
Elsevier Ltd. |
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 |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
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 |
repository.mail.fl_str_mv |
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1799136465758715904 |