Games for the two membranes problem

Autores
Miranda, Alfredo Manuel; Rossi, Julio Daniel
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We find viscosity solutions to the two membranes problem (that is, a system with two obstacle-type equations) with two different p-Laplacian operators taking limits of value functions of a sequence of games. We analyze two-player zero-sum games that are played in two boards with different rules in each board. At each turn both players (one inside each board) have the choice of playing without changing board or changing to the other board (and then playing one round of the other game). We show that the value functions corresponding to this kind of game converge uniformly to a viscosity solution of the two membranes problem. If in addition the possibility of having the choice to change boards depends on a coin toss we show that we also have convergence of the value functions to the two membranes problem that is supplemented with an extra condition inside the coincidence set.
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; Argentina
Fil: 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; Argentina
Materia
Viscosity solutions
Tug-of-War
Free boundary problem
Game theory
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:11336/256066
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/256066
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Games for the two membranes problemMiranda, Alfredo ManuelRossi, Julio DanielViscosity solutionsTug-of-WarFree boundary problemGame theoryhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We find viscosity solutions to the two membranes problem (that is, a system with two obstacle-type equations) with two different p-Laplacian operators taking limits of value functions of a sequence of games. We analyze two-player zero-sum games that are played in two boards with different rules in each board. At each turn both players (one inside each board) have the choice of playing without changing board or changing to the other board (and then playing one round of the other game). We show that the value functions corresponding to this kind of game converge uniformly to a viscosity solution of the two membranes problem. If in addition the possibility of having the choice to change boards depends on a coin toss we show that we also have convergence of the value functions to the two membranes problem that is supplemented with an extra condition inside the coincidence set.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; ArgentinaMathematical Sciences Publishers2024-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/256066Miranda, Alfredo Manuel; Rossi, Julio Daniel; Games for the two membranes problem; Mathematical Sciences Publishers; Orbita Mathematicae; 1; 1; 1-2024; 59-1012993-61442993-6152CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://msp.org/om/2024/1-1/om-v1-n1-p04-p.pdfinfo:eu-repo/semantics/altIdentifier/doi/10.2140/om.2024.1.59info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:23:40Zoai:ri.conicet.gov.ar:11336/256066instacron: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 11:23:40.439CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Games for the two membranes problem
title Games for the two membranes problem
spellingShingle Games for the two membranes problem
Miranda, Alfredo Manuel
Viscosity solutions
Tug-of-War
Free boundary problem
Game theory
title_short Games for the two membranes problem
title_full Games for the two membranes problem
title_fullStr Games for the two membranes problem
title_full_unstemmed Games for the two membranes problem
title_sort Games for the two membranes problem
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 Viscosity solutions
Tug-of-War
Free boundary problem
Game theory
topic Viscosity solutions
Tug-of-War
Free boundary problem
Game theory
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 find viscosity solutions to the two membranes problem (that is, a system with two obstacle-type equations) with two different p-Laplacian operators taking limits of value functions of a sequence of games. We analyze two-player zero-sum games that are played in two boards with different rules in each board. At each turn both players (one inside each board) have the choice of playing without changing board or changing to the other board (and then playing one round of the other game). We show that the value functions corresponding to this kind of game converge uniformly to a viscosity solution of the two membranes problem. If in addition the possibility of having the choice to change boards depends on a coin toss we show that we also have convergence of the value functions to the two membranes problem that is supplemented with an extra condition inside the coincidence set.
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; Argentina
Fil: 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; Argentina
description We find viscosity solutions to the two membranes problem (that is, a system with two obstacle-type equations) with two different p-Laplacian operators taking limits of value functions of a sequence of games. We analyze two-player zero-sum games that are played in two boards with different rules in each board. At each turn both players (one inside each board) have the choice of playing without changing board or changing to the other board (and then playing one round of the other game). We show that the value functions corresponding to this kind of game converge uniformly to a viscosity solution of the two membranes problem. If in addition the possibility of having the choice to change boards depends on a coin toss we show that we also have convergence of the value functions to the two membranes problem that is supplemented with an extra condition inside the coincidence set.
publishDate 2024
dc.date.none.fl_str_mv 2024-01
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/11336/256066
Miranda, Alfredo Manuel; Rossi, Julio Daniel; Games for the two membranes problem; Mathematical Sciences Publishers; Orbita Mathematicae; 1; 1; 1-2024; 59-101
2993-6144
2993-6152
CONICET Digital
CONICET
url http://hdl.handle.net/11336/256066
identifier_str_mv Miranda, Alfredo Manuel; Rossi, Julio Daniel; Games for the two membranes problem; Mathematical Sciences Publishers; Orbita Mathematicae; 1; 1; 1-2024; 59-101
2993-6144
2993-6152
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://msp.org/om/2024/1-1/om-v1-n1-p04-p.pdf
info:eu-repo/semantics/altIdentifier/doi/10.2140/om.2024.1.59
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
dc.publisher.none.fl_str_mv Mathematical Sciences Publishers
publisher.none.fl_str_mv Mathematical Sciences Publishers
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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