Harnack inequality for degenerate fully nonlinear parabolic equations

Vedansh Arya; Vesa Julin

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arXiv · 2506.10608

Harnack inequality for degenerate fully nonlinear parabolic equations

Vedansh Arya·Vesa Julin

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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).

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Vedansh Arya, Vesa Julin. 2025-06-12. Harnack inequality for degenerate fully nonlinear parabolic equations. https://arxiv.org/abs/2506.10608

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