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

被引:67
作者
Lu, Pency [2 ]
Ni, Lei [1 ]
Vazquez, Juan-Luis [3 ]
Villani, Cedric [4 ,5 ]
机构
[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA
[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA
[3] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain
[4] Ecole Normale Super Lyon, Inst Univ France, F-69364 Lyon 07, France
[5] Ecole Normale Super Lyon, Unite Math Pures & Appl, F-69364 Lyon 07, France
来源
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2009年 / 91卷 / 01期
关键词
Porous medium equation; Aronson-Benilan estimate; Li-Yau type estimate; Entropy formula; HEAT-EQUATION; SOBOLEV INEQUALITIES; GAS-FLOW; REGULARITY; CONTINUITY; INTERFACES; CURVATURE; BEHAVIOR;
D O I
10.1016/j.matpur.2008.09.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work we derive local gradient and Laplacian estimates of the Aronson-Benilan 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. Published by Elsevier Masson SAS.
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页码:1 / 19
页数:19
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