On minima of a functional of the gradient: upper and lower solutions

Detalhes bibliográficos
Autor(a) principal: Goncharov, Vladimir
Data de Publicação: 2006
Outros Autores: Ornelas, António
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.
id RCAP_1be23174ba9a02fe30429d04a99a7dd8
oai_identifier_str oai:dspace.uevora.pt:10174/2548
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling 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
_version_ 1799136465758715904

Registros relacionados