Harnack inequality for (p,q)-Laplacian equations uniformly degenerated in a part of domain

Abstract

We consider a (p,q)-Laplace equation with the exponent values p,q depending on the boundary which is divided into two parts by a hyperplane. Assuming that the equation is uniformly degenerate with respect to a small parameter in the part of domain where q<p, a special Harnack inequality is proved for non-negative solutions.