An existence result for the infinity laplacian with non-homogeneous Neumann boundary conditions using Tug-of-War games

Abstract

In this paper we show how to use a Tug-of-War game to obtain existence of a viscosity solution to the infinity laplacian with non-homogeneous mixed boundary conditions. For a Lipschitz and positive function $g$ there exists a viscosity solution of the mixed boundary value problem, $$\{\begin{array}{llcc}-{\Delta }_{\infty }u(x)=0& \text{in}\Omega ,\frac{\partial u}{\partial n}(x)=g(x)& \text{on}{\Gamma }_N,u(x)=0& \text{on}{\Gamma }_D.\end{array}.$$

This paper has been withdrawn due to some errors in some of the proofs

References in corpus (1)

• Tug-of-war and the infinity Laplacian

Cited by in corpus (1)

• An infinity Laplace equation with gradient term and mixed boundary conditions