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An obstacle problem for Tug-of-War games
Juan J. Manfredi, Julio D. Rossi, Stephanie J. Somersille
We consider the obstacle problem for the infinity Laplace equation. Given a Lipschitz boundary function and a Lipschitz obstacle we prove the existence and uniqueness of a super in…
Tug-of-war and infinity Laplace equation with vanishing Neumann boundary condition
Tonći Antunović, Yuval Peres, Scott Sheffield +1
We study a version of the stochastic "tug-of-war" game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function…
An infinity Laplace equation with gradient term and mixed boundary conditions
Scott N. Armstrong, Charles K. Smart, Stephanie J. Somersille
We obtain existence, uniqueness, and stability results for the modified 1-homogeneous infinity Laplace equation \[ -Δ_\infty u - β|Du| = f, \] subject to Dirichlet or mixed Dirichl…
Biased tug-of-war, the biased infinity Laplacian, and comparison with exponential cones
Yuval Peres, Gábor Pete, Stephanie Somersille
We prove that if U\subset\R^n is an open domain whose closure \overline{U} is compact in the path metric, and F is a Lipschitz function on \partial{U}, then for each β\in\R there e…