Harnack Inequality for Nonlinear Equations Driven by the Normalized Infinity-Laplacian

Abstract

This paper aims to investigate a Harnack inequality for non-negative solutions of the normalized infinity Laplacian with nonlinear absorption and gradient terms. More specifically, we establish a Harnack inequality for non-negative viscosity solutions of the PDE $\Delta_\infty^Nu=f(u)+g(u)|Du|^q$, where $0\le q\le 1$, and for a large class of non-decreasing continuous functions $f$ and $g$ that meet suitable growth conditions at infinity.