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.

37pages