Uniqueness of Viscosity Solutions to the Dirichlet Problem Involving Infinity Laplacian

Abstract

In this paper, we study the Dirichlet boundary value problem involving the highly degenerate and h-homogeneous quasilinear operator associated with the infinity Laplacian, where the right hand side term is and the boundary value is . First, we establish the comparison principle by the double variables method based on the viscosity solutions theory for the general equation in. We propose two different conditions for the right hand side and get the comparison principle results under different conditions by making different perturbations. Then, we obtain the uniqueness of the viscosity solution to the Dirichlet boundary value problem by the comparison principle. Moreover, we establish the local Lipschitz continuity of the viscosity solution.