Harnack inequality for nonlinear equations driven by the normalized infinity-Laplacian

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 ΔN∞u = f(u)+g(u)|Du|q where 0 ≤ q ≤ 1, and for a large class of non-decreasing continuous functions f and g that meet suitable growth conditions at infinity.