H\"older Continuity and Harnack estimate for non-homogeneous parabolic equations

Abstract

In this paper we continue the study on intrinsic Harnack inequality for non- homogeneous parabolic equations in non-divergence form initiated by the first author in [1]. We establish a forward-in-time intrinsic Harnack inequality, which in particular implies the H\"older continuity of the solutions. We also provide a Harnack type estimate on global scale which quantifies the strong minimum principle. In the time-independent setting, this together with [1] provides an alternative proof of the generalized Harnack inequality proven by the second author in [9].