Tug-of-War games and the infinity Laplacian with spatial dependence

IVANA GÓMEZ; JULIO DANIEL ROSSI

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS

AMER INST MATHEMATICAL SCIENCES

Lugar: Springfield; Año: 2012

1534-0392

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. Inthis way we find existence of viscosity solutions to the Dirichlet problem for an equation of the form$- langle D^2 vcdot J_x(D v) ;  J_x(Dv) angle (x) =0$, that is, an infinity Laplacian with spatial dependence. Here $J_x (Dv(x))$ is a vector that depends on the spatial location and the gradient of the solution.