Local Aronson-B\'enilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds
Differential Geometry
2008-06-09 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.0806.1142,
title = {Local Aronson-B\'enilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds},
author = {Peng Lu and Lei Ni and Juan-Luis Vázquez and Cédric Villani},
journal= {arXiv preprint arXiv:0806.1142},
year = {2008}
}
Comments
22 pages, no figure