Stability for the infinity-laplace equation with variable exponent

Abstract

We study the stability for the viscosity solutions of the differential equation $$ \sum u_{x_i}u_{x_j}u_{x_i x_j}+ | {\nabla u} | ^2\ln( | {\nabla u} | )\langle\nabla u, \nabla \ln p \rangle=0 $$ under perturbations of the function $p(x).$ The differential operator is the so-called $\infty(x)$-Laplacian.