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arXiv · 2608.21213

Differential Harnack Estimates for the Filtration Equations on Riemannian Manifolds via Nash--Moser Iteration

Jian-Hua Hao·Yu-Zhao Wang
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Abstract

We prove local differential Harnack estimates for smooth positive solutions of the Filtration Equations $u_t=\Delta F(u)$ on complete Riemannian manifolds in uniformly parabolic ranges. A Bochner--discriminant argument gives a coercive positive-part inequality, which is closed by Nash--Moser iteration. We derive Harnack and Liouville consequences, recover the Aronson-B\'enilan estimates for porous medium equation and fast diffusion equation, and describe a class of genuinely non-power filtration laws.

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Jian-Hua Hao, Yu-Zhao Wang. 2026-08-21. Differential Harnack Estimates for the Filtration Equations on Riemannian Manifolds via Nash--Moser Iteration. https://arxiv.org/abs/2608.21213

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