PreprintCC BY 4.0arXiv
Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds
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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BibTeX
@misc{hao2026differential,
title = {{Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds}},
author = {Jian-Hua Hao and Yu-Zhao Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.21213},
eprint = {2608.21213},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.21213},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Differential Harnack Estimates and Frequency Monotonicity for Filtration Equations on Riemannian Manifolds
AU - Jian-Hua Hao
AU - Yu-Zhao Wang
PY - 2026
DA - 2026/09/19
PB - arXiv
DO - 10.48550/arxiv.2608.21213
UR - https://arxiv.org/abs/2608.21213
AB - 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.
ER -