Differential Harnack Estimates and Entropy Formulae for Weighted p-Heat Equations

被引：0
作者：
Wang, Yu-Zhao [1 ]
机构：
[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2017年 / 71卷 / 3-4期
基金：
美国国家科学基金会;
关键词：
Weighted p-heat equations; W-entropy formula; gradient estimate; differential Harnack estimate; Bakry-Emery Ricci curvature; NONLINEAR DIFFUSION-EQUATIONS; COMPLETE RIEMANNIAN-MANIFOLDS; WITTEN LAPLACIAN; POROUS-MEDIUM;
D O I：
10.1007/s00025-017-0675-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we obtain various global differential Harnack estimates for positive solutions to weighted p-heat equation on closed smooth metric measure space with a lower m-Bakry-Eemery Ricci curvature bound. Moreover, Perelman type W-entropy formulae and Li-Yau type entropy inequalities are derived for weighted p-heat equation on compact with boundary (or no boundary) smooth metric measure space with nonnegative (or negative) m-Bakry-Eemery Ricci curvature, which are new in non-weighted case and generalized the results of Kotschwar and Ni (Ann Sci ec Norm Super 42(1):1-36, 2009) and Wang et al. (Acta Math Sci Ser B Engl Ed 33(4):963-974, 2013).
引用
收藏
页码：1499 / 1520
页数：22
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