Obstacle problem and maximal operators

Autores
Blanc, Pablo; Pinasco, Juan Pablo; Rossi, Julio Daniel
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li (i=1,2 alternating them) with obstacle given by the previous term un−1 in a domain Ω and a fixed boundary datum g on ∂Ω. We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L1u,L2u}=0 in Ω with u=g on ∂Ω.
Fil: Blanc, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Pinasco, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Materia
tug of war
maximal operators
obstable problem
fully nonlinear operators
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:11336/55423
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/55423
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Obstacle problem and maximal operatorsBlanc, PabloPinasco, Juan PabloRossi, Julio Danieltug of warmaximal operatorsobstable problemfully nonlinear operatorshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li (i=1,2 alternating them) with obstacle given by the previous term un−1 in a domain Ω and a fixed boundary datum g on ∂Ω. We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L1u,L2u}=0 in Ω with u=g on ∂Ω.Fil: Blanc, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Pinasco, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaFil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; ArgentinaDe Gruyter2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/55423Blanc, Pablo; Pinasco, Juan Pablo; Rossi, Julio Daniel; Obstacle problem and maximal operators; De Gruyter; Advanced Nonlinear Studies; 16; 2; 1-2016; 355-3621536-1365CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2015-5044info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.ahead-of-print/ans-2015-5044/ans-2015-5044.xmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:04:35Zoai:ri.conicet.gov.ar:11336/55423instacron: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:34982025-10-22 11:04:35.553CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Obstacle problem and maximal operators
title Obstacle problem and maximal operators
spellingShingle Obstacle problem and maximal operators
Blanc, Pablo
tug of war
maximal operators
obstable problem
fully nonlinear operators
title_short Obstacle problem and maximal operators
title_full Obstacle problem and maximal operators
title_fullStr Obstacle problem and maximal operators
title_full_unstemmed Obstacle problem and maximal operators
title_sort Obstacle problem and maximal operators
dc.creator.none.fl_str_mv Blanc, Pablo
Pinasco, Juan Pablo
Rossi, Julio Daniel
author Blanc, Pablo
author_facet Blanc, Pablo
Pinasco, Juan Pablo
Rossi, Julio Daniel
author_role author
author2 Pinasco, Juan Pablo
Rossi, Julio Daniel
author2_role author
author
dc.subject.none.fl_str_mv tug of war
maximal operators
obstable problem
fully nonlinear operators
topic tug of war
maximal operators
obstable problem
fully nonlinear operators
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li (i=1,2 alternating them) with obstacle given by the previous term un−1 in a domain Ω and a fixed boundary datum g on ∂Ω. We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L1u,L2u}=0 in Ω with u=g on ∂Ω.
Fil: Blanc, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Pinasco, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
Fil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas ; Argentina
description Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li (i=1,2 alternating them) with obstacle given by the previous term un−1 in a domain Ω and a fixed boundary datum g on ∂Ω. We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L1u,L2u}=0 in Ω with u=g on ∂Ω.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
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/11336/55423
Blanc, Pablo; Pinasco, Juan Pablo; Rossi, Julio Daniel; Obstacle problem and maximal operators; De Gruyter; Advanced Nonlinear Studies; 16; 2; 1-2016; 355-362
1536-1365
CONICET Digital
CONICET
url http://hdl.handle.net/11336/55423
identifier_str_mv Blanc, Pablo; Pinasco, Juan Pablo; Rossi, Julio Daniel; Obstacle problem and maximal operators; De Gruyter; Advanced Nonlinear Studies; 16; 2; 1-2016; 355-362
1536-1365
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1515/ans-2015-5044
info:eu-repo/semantics/altIdentifier/url/https://www.degruyter.com/view/j/ans.ahead-of-print/ans-2015-5044/ans-2015-5044.xml
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
dc.publisher.none.fl_str_mv De Gruyter
publisher.none.fl_str_mv De Gruyter
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 12.982451

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