Hölder continuity and Harnack estimate for non-homogeneous parabolic equations (Q6670379)

In this paper, the authors extend the results obtained in a previous paper by the first author on the intrinsic Harnack inequality for non-homogeneous parabolic equations in non-divergence form. A forward-in-time intrinsic Harnack inequality is proved. This intrinsic inequality implies Hölder continuity of the solutions. A global-scale Harnack-type estimate that quantifies the strong minimum principle is also established. In the time-independent setting, this result, together with those proved in the previous paper, provides an alternative proof of a generalized Harnack inequality proved by the second author.