A game theoretical approximation for a parabolic/elliptic system with different operators

In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and involves the usual Laplacian. We prove that there is a two-player zero-sum game played in two different boards...

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Detalles Bibliográficos
Autores: Miranda, Alfredo Manuel, Rossi, Julio Daniel
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2022
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/162769
Acceso en línea:http://hdl.handle.net/11336/162769
Access Level:acceso abierto
Palabra clave:PARABOLIC
ELLIPTIC
VISCOSITY SOLUTION
PROBABILISTIC APPROACH
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling A game theoretical approximation for a parabolic/elliptic system with different operatorsMiranda, Alfredo ManuelRossi, Julio DanielPARABOLICELLIPTICVISCOSITY SOLUTIONPROBABILISTIC APPROACHhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and involves the usual Laplacian. We prove that there is a two-player zero-sum game played in two different boards with different rules in each board (in the first one we play a Tug-of-War game taking the number of plays into consideration and in the second board we move at random) whose value functions converge uniformly to a viscosity solution to the PDE system.Fil: Miranda, Alfredo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Rossi, Julio Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaAmerican Institute of Mathematical Sciences2022-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/162769Miranda, Alfredo Manuel; Rossi, Julio Daniel; A game theoretical approximation for a parabolic/elliptic system with different operators; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 2022; 1-2022; 1-321078-0947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/dcds.2022034info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2022034info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:51:50Zoai:ri.conicet.gov.ar:11336/162769instacron: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:34982024-05-08 13:51:50.398CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A game theoretical approximation for a parabolic/elliptic system with different operators
title A game theoretical approximation for a parabolic/elliptic system with different operators
spellingShingle A game theoretical approximation for a parabolic/elliptic system with different operators
Miranda, Alfredo Manuel
PARABOLIC
ELLIPTIC
VISCOSITY SOLUTION
PROBABILISTIC APPROACH
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short A game theoretical approximation for a parabolic/elliptic system with different operators
title_full A game theoretical approximation for a parabolic/elliptic system with different operators
title_fullStr A game theoretical approximation for a parabolic/elliptic system with different operators
title_full_unstemmed A game theoretical approximation for a parabolic/elliptic system with different operators
title_sort A game theoretical approximation for a parabolic/elliptic system with different operators
dc.creator.none.fl_str_mv Miranda, Alfredo Manuel
Rossi, Julio Daniel
author Miranda, Alfredo Manuel
author_facet Miranda, Alfredo Manuel
Rossi, Julio Daniel
author_role author
author2 Rossi, Julio Daniel
author2_role author
dc.subject.none.fl_str_mv PARABOLIC
ELLIPTIC
VISCOSITY SOLUTION
PROBABILISTIC APPROACH
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic PARABOLIC
ELLIPTIC
VISCOSITY SOLUTION
PROBABILISTIC APPROACH
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and involves the usual Laplacian. We prove that there is a two-player zero-sum game played in two different boards with different rules in each board (in the first one we play a Tug-of-War game taking the number of plays into consideration and in the second board we move at random) whose value functions converge uniformly to a viscosity solution to the PDE system.
publishDate 2022
dc.date.none.fl_str_mv 2022-01
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/11336/162769
Miranda, Alfredo Manuel; Rossi, Julio Daniel; A game theoretical approximation for a parabolic/elliptic system with different operators; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 2022; 1-2022; 1-32
1078-0947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/162769
identifier_str_mv Miranda, Alfredo Manuel; Rossi, Julio Daniel; A game theoretical approximation for a parabolic/elliptic system with different operators; American Institute of Mathematical Sciences; Discrete And Continuous Dynamical Systems; 2022; 1-2022; 1-32
1078-0947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/dcds.2022034
info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2022034
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,811543

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