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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/256066
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T09:54:21Zoai: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:34982025-09-29 09:54:22.153CONICET 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 |
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CONICET Digital (CONICET) |
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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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13.070432 |