Harnack inequality for non-divergence structure semi-linear elliptic equations

Abstract

In this paper we establish a Harnack inequality for non-negative solutions of L⁢u=f⁢(u){Lu=f(u)} where L is a non-divergence structure uniformly elliptic operator and f is a non-decreasing function that satisfies an appropriate growth conditions at infinity.

Keywords

• non-divergence structure elliptic operator
• harnack inequality
• large solution, alexandroff–bakelman–pucci maximum principle