Abstract
Given a bounded $\mathcal{C}^{2}$ domain G⊂ℝm, functions $g\in\mathcal{C}(\partial G,{\mathbb{R}})$ and $h\in\mathcal {C}(\overline{G},{\mathbb{R}}\setminus\{0\})$, let u denote the unique viscosity solution to the equation −2Δ∞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.
Citation
Rami Atar. Amarjit Budhiraja. "A stochastic differential game for the inhomogeneous ∞-Laplace equation." Ann. Probab. 38 (2) 498 - 531, March 2010. https://doi.org/10.1214/09-AOP494
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