A desigualdade de Harnack e a Hölder continuidade para funções g-harmônicas.

Abstract

In this dissertation work, we investigated Harnack's inequality for G-harmonic functions, that is, functions that are weak solutions of the partial differential equation \Delta_gu=0. Here, the function g:[0, \infty) \rightarrow {\mathbb{R}} is the derivative of an appropriate N-function. The \Delta_g operator can be seen as a natural generalization of the Laplacian operator and its nonlinear analogue called the p-Laplacian. We assume that the function g satisfies regularity conditions introduced by G.Lieberman and we use J.Moser's iteration method (Moser iteration technique) to conclude that such functions (weak solutions) are locally \alpha-Hölder continuous.