Harnack inequality for a p-Laplacian equation with a source reaction term involving the product of the function and its gradient

Abstract

A p-Laplacian type problem with a source reaction term involving the product of the function and its gradient is considered in this paper. A Harnack inequality is proved, and the main idea is based on de Giorgi-Nash-Moser iteration and Moser's iteration technique. As a consequence, $ H\ddot{o}lder $ continuity and boundness for the solution of this problem also are obtained.

Keywords

• p-laplace
• harnack inequality
• de giorgi-nash-moser iteration
• moser's iteration