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arXiv · 0808.1457

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

Rami Atar·Amarjit Budhiraja
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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.

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Rami Atar, Amarjit Budhiraja. 2008-08-11. A stochastic differential game for the inhomogeneous $\infty$-Laplace equation. https://doi.org/10.1214/09-aop494

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