Harnack's inequality for p-Laplacian equations with Muckenhoupt weight degenerating in part of the domain

Abstract

In this article we consider quasi-linear second-order elliptic equations of divergence structure with Makenhaupt weight that degenerates over a small part of the domain. We show that the classical Harnack's inequality does not hold in this case, and prove an appropriate Harnack's inequality for the considered equation.