On the Dirichlet problem for solutions of a restricted nonlinear mean value property

Abstract

We give an analytic proof of the solution of Dirichlet Problem for continous functions satisfying a nonlinear mean value problem related to the p-laplace operator and certain stochastic games.

A dynamic programming principle with continuous solutions related to the $p$-Laplacian, $1 < p < \infty$

“…The groundwork was laid in the seminal papers [16,17]. Game-theoretic views have since led to simplified proof of theorems concerning p-and ∞-harmonic functions, as in [3,11], as well as stimulated plenty of other related research, as in [1,2,4,5,6,9,10,12,13,14,15,18].…”