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
Descripción
Sumario: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.