Hölder continuity and the Harnack inequality for the solutions of an elliptic equation containing the $p$ -Laplacian and uniformly degenerating in a part of the domain

Abstract

We consider quasilinear equations of the $p$-Laplacian type uniformly degenerating in a part of the domain. An analog of the Harnack inequality is proved for nonnegative solutions and the Holder continuity of the solutions is established by using this inequality.