Remarks on differential Harnack inequalities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Qian, Bin

关键词: Heat equations;    Differential Harnack inequalities;    Gradient estimates;    Entropy;   

DOI  :  10.1016/j.jmaa.2013.07.043

来源: Elsevier

【 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.

【 授权许可】

Free