Convergence of dynamic programming principles for the $p$-Laplacian

Abstract

We provide a unified strategy to show that solutions of dynamic programming principles associated to the $p$-Laplacian converge to the solution of the corresponding Dirichlet problem. Our approach includes all previously known cases for continuous and discrete dynamic programming principles, provides new results, and gives a convergence proof free of probability arguments.

28 pages, 1 figure. Accepted for publication in Advances in Calculus of Variations