Remarks on differential Harnack inequalities

被引：28

作者：

Qian, Bin ^{[1
]}

机构：

[1] Changshu Inst Technol, Dept Math, Changshu 215500, Jiangsu, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 409卷 / 01期

关键词：

Heat equations; Differential Harnack inequalities; Gradient estimates; Entropy; EQUATIONS;

D O I：

10.1016/j.jmaa.2013.07.043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we give a generalization of (global and local) differential Harnack inequalities for heat equations obtained by Li and Xu [J.F. Li, X.J. Xu, Differential Harnack inequalities on Riemannian manifolds I: linear heat equation, Adv: Math. 226 (5) (2011) 4456-4491] and Baudoin and Garofalo [F. Baudoin, N. Garofalo, Perelman's entropy and doubling property on Riemannian manifolds, J. Geom. Anal. 21 (2011) 1119-1131]. From this we can derive new Harnack inequalities and new lower bounds for the associated heat kernel. Also we provide some new entropy formulas with monotonicity. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：556 / 566

页数：11

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