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

TL;DR

This paper provides an analytic proof for solving the Dirichlet problem for continuous functions that satisfy a nonlinear mean value property connected to the p-Laplace operator and stochastic games.

Contribution

It offers a new analytic proof for the Dirichlet problem solutions involving nonlinear mean value properties related to the p-Laplace operator.

Findings

Analytic proof of Dirichlet problem solutions

Connection to stochastic games established

Applicable to continuous functions with nonlinear mean value properties

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.