Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds

Details Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds

2008-06-06

arxiv.org/abs/0806.1142v1

Mathematics

Differential Geometry

22 pages, no figure

Scientific paper

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.

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