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arXiv · 2608.21213

Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds

Jian-Hua Hao·Yu-Zhao Wang
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Abstract

In this work we derive local differential Harnack estimates for positive solutions of filtration equations on complete Riemannian manifolds with a lower Ricci curvature bound by using Nash--Moser iteration. Inspired by earlier work on parabolic frequency functions, we establish some new frequency monotonicity formulas for these equations. The results cover the porous-medium and fast-diffusion equations, as well as several non-power diffusion laws.

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Jian-Hua Hao, Yu-Zhao Wang. 2026-09-19. Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds. https://arxiv.org/abs/2608.21213

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