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arXiv · 0806.1142

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

Peng Lu·Lei Ni·Juan-Luis Vázquez·Cédric Villani
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Abstract

In this work we derive local gradient and Laplacian estimates of the Aronson-Bénilan 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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Peng Lu, Lei Ni, Juan-Luis Vázquez, Cédric Villani. 2008-06-06. Local Aronson-Bénilan estimates and entropy formulae for porous medium and fast diffusion equations on manifolds. https://arxiv.org/abs/0806.1142

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