Affordable Access

Local Aronson-B\'enilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds

Authors
Type
Preprint
Publication Date
Submission Date
Source
arXiv
License
Yellow
External links

Abstract

In this work we derive local gradient and Laplacian estimates of the Aronson-B\'enilan and Li-Yau type for positive solutions of porous medium equations posed on Riemannian manifolds with a lower Ricci curvature bound. We also prove similar results for some fast diffusion equations. Inspired by Perelman's work we discover some new entropy formulae for these equations.

Statistics

Seen <100 times