A minimum problem with free boundary in Orlicz spaces

Autores
Martinez, Sandra Rita; Wolanski, Noemi Irene
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the minimization problem: int_Omega ?G(|nabla u), dx +|{u>0}|) in u-u_0 in W_0^{1,G}(Omega) for a given u_0 in W_0^{1,G}(Omega). The conditions on the function G allow for different behavior at 0 and infinity. We prove that every solution is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, is a regular surface. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C^{1,alpha} regularity of their free boundaries near flat  free boundary points.
Fil: Martinez, Sandra Rita. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
FREE BOUNDARIES
ORLICZ SPACES
MINIMIZATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/275189
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/275189
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A minimum problem with free boundary in Orlicz spacesMartinez, Sandra RitaWolanski, Noemi IreneFREE BOUNDARIESORLICZ SPACESMINIMIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the minimization problem: int_Omega ?G(|nabla u), dx +|{u>0}|) in u-u_0 in W_0^{1,G}(Omega) for a given u_0 in W_0^{1,G}(Omega). The conditions on the function G allow for different behavior at 0 and infinity. We prove that every solution is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, is a regular surface. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C^{1,alpha} regularity of their free boundaries near flat  free boundary points.Fil: Martinez, Sandra Rita. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAcademic Press Inc Elsevier Science2008-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/275189Martinez, Sandra Rita; Wolanski, Noemi Irene; A minimum problem with free boundary in Orlicz spaces; Academic Press Inc Elsevier Science; Advances in Mathematics; 218; 6; 5-2008; 1914-19710001-8708CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2008.03.028info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870808000984?via%3Dihubinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-03T08:54:51Zoai:ri.conicet.gov.ar:11336/275189instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-12-03 08:54:51.36CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A minimum problem with free boundary in Orlicz spaces
title A minimum problem with free boundary in Orlicz spaces
spellingShingle A minimum problem with free boundary in Orlicz spaces
Martinez, Sandra Rita
FREE BOUNDARIES
ORLICZ SPACES
MINIMIZATION
title_short A minimum problem with free boundary in Orlicz spaces
title_full A minimum problem with free boundary in Orlicz spaces
title_fullStr A minimum problem with free boundary in Orlicz spaces
title_full_unstemmed A minimum problem with free boundary in Orlicz spaces
title_sort A minimum problem with free boundary in Orlicz spaces
dc.creator.none.fl_str_mv Martinez, Sandra Rita
Wolanski, Noemi Irene
author Martinez, Sandra Rita
author_facet Martinez, Sandra Rita
Wolanski, Noemi Irene
author_role author
author2 Wolanski, Noemi Irene
author2_role author
dc.subject.none.fl_str_mv FREE BOUNDARIES
ORLICZ SPACES
MINIMIZATION
topic FREE BOUNDARIES
ORLICZ SPACES
MINIMIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider the minimization problem: int_Omega ?G(|nabla u), dx +|{u>0}|) in u-u_0 in W_0^{1,G}(Omega) for a given u_0 in W_0^{1,G}(Omega). The conditions on the function G allow for different behavior at 0 and infinity. We prove that every solution is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, is a regular surface. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C^{1,alpha} regularity of their free boundaries near flat  free boundary points.
Fil: Martinez, Sandra Rita. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We consider the minimization problem: int_Omega ?G(|nabla u), dx +|{u>0}|) in u-u_0 in W_0^{1,G}(Omega) for a given u_0 in W_0^{1,G}(Omega). The conditions on the function G allow for different behavior at 0 and infinity. We prove that every solution is locally Lipschitz continuous, that it is a solution to a free boundary problem and that the free boundary, is a regular surface. Also, we introduce the notion of weak solution to the free boundary problem solved by the minimizers and prove the Lipschitz regularity of the weak solutions and the C^{1,alpha} regularity of their free boundaries near flat  free boundary points.
publishDate 2008
dc.date.none.fl_str_mv 2008-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/275189
Martinez, Sandra Rita; Wolanski, Noemi Irene; A minimum problem with free boundary in Orlicz spaces; Academic Press Inc Elsevier Science; Advances in Mathematics; 218; 6; 5-2008; 1914-1971
0001-8708
CONICET Digital
CONICET
url http://hdl.handle.net/11336/275189
identifier_str_mv Martinez, Sandra Rita; Wolanski, Noemi Irene; A minimum problem with free boundary in Orlicz spaces; Academic Press Inc Elsevier Science; Advances in Mathematics; 218; 6; 5-2008; 1914-1971
0001-8708
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.aim.2008.03.028
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870808000984?via%3Dihub
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.275514

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