2015/11/05 by Luca Codenotti, Marta Lewicka, Codenotti, Luca +3
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP
paper · pdf · doi:10.48550/arxiv.1511.01604
16 pages, 5 figures
arxiv created 2015/11/05 · arxiv updated 2015/11/06
We study the double-obstacle problem for the p-Laplace operator, p 2 [2;1). We prove that for Lipschitz boundary data and Lipschitz obstacles, viscosity solutions are unique and coincide with variational solutions. They are also uniform limits of solutions to discrete min-max problems that can be interpreted as the dynamic programming principle for appropriate tug-ofwar games with noise. In these games, both players in addition to choosing their strategies, are also allowed to choose stopping times. The solutions to the double-obstacle problems are limits of values of these games, when the step-size controlling the single shift in the token's position, converges to 0. We propose a numerical scheme based on this observation and show how it works for some examples of obstacles and boundary data.