Harnack inequality for degenerate fully nonlinear parabolic equations

TL;DR

This paper establishes Harnack inequalities for degenerate fully nonlinear parabolic equations in nondivergence form, extending classical results to a broader class of nonlinear PDEs with degeneracy.

Contribution

It proves intrinsic and weak Harnack inequalities for nonnegative solutions and supersolutions, generalizing previous divergence form results to nondivergence form equations.

Findings

Proved intrinsic Harnack inequality for solutions.

Established weak Harnack inequality for supersolutions.

Extended classical results to degenerate fully nonlinear nondivergence equations.

Abstract

We consider degenerate fully nonlinear parabolic equations, which generalize the p-parabolic equation with $p>2$ to nondivergence form operators. We prove an intrinsic Harnack inequality for nonnegative solutions and a weak Harnack inequality for nonnegative supersolutions. These results can be seen as the nondivergence form counterparts of the results by DiBenedetto, Gianazza and Vespri (Acta Math. 2008) and Kuusi (Ann. Sc. Norm. Super. Pisa 2008).