Convergence of convex sets with gradient constraint

Detalhes bibliográficos
Autor(a) principal: Azevedo, Assis
Data de Publicação: 2004
Outros Autores: Santos, Lisa
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/1822/2899
Resumo: Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.
id RCAP_dbd0c86db971b09ece35165b367d7058
oai_identifier_str oai:repositorium.sdum.uminho.pt:1822/2899
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Convergence of convex sets with gradient constraintMosco convergenceQuasivariational inequalityScience & TechnologyGiven a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação (POCTI), União Europeia (UE). Fundo Europeu de Desenvolvimento Regional - (Portugal/FEDER-EU).Heldermann VerlagUniversidade do MinhoAzevedo, AssisSantos, Lisa20042004-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/2899eng"Journal of Convex Analysis". ISSN 0944-6532. 11:2 (2004) 285-301.0944-6532info: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:RCAAP2023-07-21T11:56:24Zoai:repositorium.sdum.uminho.pt:1822/2899Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T18:46:00.430507Repositório 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 Convergence of convex sets with gradient constraint
title Convergence of convex sets with gradient constraint
spellingShingle Convergence of convex sets with gradient constraint
Azevedo, Assis
Mosco convergence
Quasivariational inequality
Science & Technology
title_short Convergence of convex sets with gradient constraint
title_full Convergence of convex sets with gradient constraint
title_fullStr Convergence of convex sets with gradient constraint
title_full_unstemmed Convergence of convex sets with gradient constraint
title_sort Convergence of convex sets with gradient constraint
author Azevedo, Assis
author_facet Azevedo, Assis
Santos, Lisa
author_role author
author2 Santos, Lisa
author2_role author
dc.contributor.none.fl_str_mv Universidade do Minho
dc.contributor.author.fl_str_mv Azevedo, Assis
Santos, Lisa
dc.subject.por.fl_str_mv Mosco convergence
Quasivariational inequality
Science & Technology
topic Mosco convergence
Quasivariational inequality
Science & Technology
description Given a bounded open subset of R^N, we study the convergence of a sequence (K_n)_{n\in\N} of closed convex subsets of W_0^{1,p}(\Omega) (p\in]1,\infty[) with gradient constraint, to a convex set K, in the Mosco sense. A particular case of the problem studied is when K_n={v\in W_0^{1,p}(\Omega):: F_n(x,\nabla v(x))<= g_n(x) for a.e. x in \Omega}. Some examples of non-convergence are presented. We also present an improvement of a result of existence of a solution of a quasivariational inequality, as an application of this Mosco convergence result.
publishDate 2004
dc.date.none.fl_str_mv 2004
2004-01-01T00:00:00Z
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/1822/2899
url http://hdl.handle.net/1822/2899
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv "Journal of Convex Analysis". ISSN 0944-6532. 11:2 (2004) 285-301.
0944-6532
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Heldermann Verlag
publisher.none.fl_str_mv Heldermann Verlag
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_ 1799132214070345728

Registros relacionados