Random extremal solutions of differential inclusions

Detalhes bibliográficos
Autor(a) principal: Bressan, Alberto
Data de Publicação: 2016
Outros Autores: Staicu, Vasile
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/15704
Resumo: Given a Lipschitz continuous multifunction $F$ on ${\mathbb{R}}^{n}$, we construct a probability measure on the set of all solutions to the Cauchy problem $\dot x\in F(x)$ with $x(0)=0$. With probability one, the derivatives of these random solutions take values within the set $ext F(x)$ of extreme points for a.e.~time $t$. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.
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spelling Random extremal solutions of differential inclusionsDifferential inclusionsLipschitz selectionsExtremal solutionsRandom solutionsGiven a Lipschitz continuous multifunction $F$ on ${\mathbb{R}}^{n}$, we construct a probability measure on the set of all solutions to the Cauchy problem $\dot x\in F(x)$ with $x(0)=0$. With probability one, the derivatives of these random solutions take values within the set $ext F(x)$ of extreme points for a.e.~time $t$. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.Springer2016-06-13T09:59:14Z2016-06-01T00:00:00Z2016-06info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/15704eng1021-972210.1007/s00030-016-0375-0Bressan, AlbertoStaicu, Vasileinfo: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:RCAAP2024-02-22T11:28:09Zoai:ria.ua.pt:10773/15704Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:50:38.923319Repositório 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 Random extremal solutions of differential inclusions
title Random extremal solutions of differential inclusions
spellingShingle Random extremal solutions of differential inclusions
Bressan, Alberto
Differential inclusions
Lipschitz selections
Extremal solutions
Random solutions
title_short Random extremal solutions of differential inclusions
title_full Random extremal solutions of differential inclusions
title_fullStr Random extremal solutions of differential inclusions
title_full_unstemmed Random extremal solutions of differential inclusions
title_sort Random extremal solutions of differential inclusions
author Bressan, Alberto
author_facet Bressan, Alberto
Staicu, Vasile
author_role author
author2 Staicu, Vasile
author2_role author
dc.contributor.author.fl_str_mv Bressan, Alberto
Staicu, Vasile
dc.subject.por.fl_str_mv Differential inclusions
Lipschitz selections
Extremal solutions
Random solutions
topic Differential inclusions
Lipschitz selections
Extremal solutions
Random solutions
description Given a Lipschitz continuous multifunction $F$ on ${\mathbb{R}}^{n}$, we construct a probability measure on the set of all solutions to the Cauchy problem $\dot x\in F(x)$ with $x(0)=0$. With probability one, the derivatives of these random solutions take values within the set $ext F(x)$ of extreme points for a.e.~time $t$. This provides an alternative approach in the analysis of solutions to differential inclusions with non-convex right hand side.
publishDate 2016
dc.date.none.fl_str_mv 2016-06-13T09:59:14Z
2016-06-01T00:00:00Z
2016-06
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/10773/15704
url http://hdl.handle.net/10773/15704
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 1021-9722
10.1007/s00030-016-0375-0
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 Springer
publisher.none.fl_str_mv Springer
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
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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
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