The Infinity Laplace Equation

Abstract

In this thesis, we prove that the Infinity-Laplace equation has a unique solution in the viscosity sense. We prove existence by approximating the equation by the p-Laplace equation, and uniqueness will be shown by use of the Theorem on Sums. We will also show that the viscosity solutions of the Infinity-Laplace equation enjoys comparison with cones, and vice versa.