Gradient estimates and Harnack inequalities of a nonlinear parabolic equation for the V-Laplacian

被引：12

作者：

Chen, Qun ^{[1
]}

Qiu, Hongbing ^{[1
,2
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2016年 / 50卷 / 01期

关键词：

Gradient estimate; Nonlinear parabolic equation; Positive solution; Harnack inequality;

D O I：

10.1007/s10455-016-9501-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider gradient estimates for the positive solutions to the following nonlinear parabolic equation: on M x [0, T], where a is a real constant. We obtain the Li-Yau type bounds of the above equation, which cover the estimates in Davies (Heat kernels and spectral theory 1989), Huang et al. (Ann GlobAnalGeom 43: 209-232, 2013), Li andXu (Adv Math 226: 4456-4491, 2011) and Qian (J Math Anal Appl 409: 556-566, 2014). Besides, as a corollary, we give a gradient estimate for the corresponding elliptic case: which improves the estimates in Chen and Chen (Ann Glob Anal Geom 35: 397-404, 2009) and Yang (Proc AMS 136(11): 4095-4102, 2008).

引用

页码：47 / 64

页数：18

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