Elliptic Harnack's inequality for a singular nonlinear parabolic equation in non-divergence form

TL;DR

This paper establishes an elliptic Harnack's inequality for a broad class of nonlinear parabolic equations, including the p-Laplace and stochastic game theory variants, without needing intrinsic waiting time.

Contribution

It introduces a new form of Harnack's inequality applicable to general nonlinear parabolic equations in non-divergence form, removing the intrinsic waiting time requirement.

Findings

Proves elliptic Harnack's inequality for generalized parabolic equations

Extends applicability to equations in non-divergence form

Provides estimates with same time level on both sides

Abstract

We prove an elliptic Harnack's inequality for a general form of a parabolic equation that generalizes both the standard parabolic $p$-Laplace equation and the normalized version that has been proposed in stochastic game theory. This version of the inequality doesn't require the intrinsic waiting time and we get the estimate with the same time level on both sides of the inequality.