Tug-of-War games and the infinity Laplacian with spatial dependence
In this paper we look for PDEs that arise as limits of values of Tug-of-War games when the possible movements of the game are taken in a family of sets that are not necessarily euclidean balls. In this way we ¯nd existence of viscosity solutions to the Dirichlet problem for an equation of the form ¡...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | Argentina |
| Institución: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repositorio: | CONICET Digital (CONICET) |
| Idioma: | inglés |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/1067 |
| Acceso en línea: | http://hdl.handle.net/11336/1067 |
| Access Level: | acceso abierto |
| Palabra clave: | elliptic problems https://purl.org/becyt/ford/1 https://purl.org/becyt/ford/1.1 |
| Sumario: | In this paper we look for PDEs that arise as limits of values of Tug-of-War games when the possible movements of the game are taken in a family of sets that are not necessarily euclidean balls. In this way we ¯nd existence of viscosity solutions to the Dirichlet problem for an equation of the form ¡hD 2 v ¢ Jx(Dv); Jx(Dv)i(x) = 0, that is, an in¯nity Laplacian with spatial dependence. Here Jx(Dv(x)) is a vector that depends on the the spatial location and the gradient of the solution. |
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