A stochastic differential game for the inhomogeneous $\infty$-Laplace equation

Abstract

Given a bounded $\mathcaligr{C}^2$ domain $G\subset {\mathbb{R}}^m$, functions $g\in\mathcaligr{C}(\partial G,{\mathbb{R}})$ and $h\in\mathcaligr {C}(\bar{G},{\mathbb{R}}\setminus\{0\})$, let $u$ denote the unique viscosity solution to the equation $-2{\Delta }_{\infty }u=h$ in $G$ with boundary data $g$. We provide a representation for $u$ as the value of a two-player zero-sum stochastic differential game.

Published in at http://dx.doi.org/10.1214/09-AOP494 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Tug-of-war and the infinity Laplacian

Cited by in corpus (2)

• A continuous time tug-of-war game for parabolic $p(x,t)$-Laplace type equations
• Uniform measure density condition and game regularity for tug-of-war games