GRADIENT ESTIMATE FOR A NONLINEAR HEAT EQUATION ON RIEMANNIAN MANIFOLDS

被引：15

作者：

Jiang, Xinrong ^{[1
]}

机构：

[1] Jiangxi Normal Univ, Inst Math & Informat Sci, Nanchang 330022, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 08期

关键词：

Gradient estimate; nonlinear heat equation; Riemannian manifold; THEOREM;

D O I：

10.1090/proc/12995

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we derive a local Hamilton type gradient estimate for a nonlinear heat equation on Riemannian manifolds. As its application, we obtain a Liouville type theorem.

引用

页码：3635 / 3642

页数：8

共 15 条

[1] A Liouville-Type Theorem for Smooth Metric Measure Spaces [J].

Brighton, Kevin .

JOURNAL OF GEOMETRIC ANALYSIS, 2013, 23 (02) :562-570

[2] Differential Harnack estimates for a nonlinear heat equation [J].

Cao, Xiaodong ;

Ljungberg, Benjamin Fayyazuddin ;

Liu, Bowei .

JOURNAL OF FUNCTIONAL ANALYSIS, 2013, 265 (10) :2312-2330

[3]

Hamilton R. S., 1993, COMMUN ANAL GEOM, V1, P113

[4] Gradient estimate for the degenerate parabolic equation ut=ΔF(u)+H(u) on manifolds [J].

Ma, Li ;

Zhao, Lin ;

Song, Xianfa .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 244 (05) :1157-1177

[5] Gradient estimates for a simple elliptic equation on complete non-compact Riemannian manifolds [J].

Ma, Li .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 241 (01) :374-382

[6]

Schoen R., 1994, C P LECT NOTES GEOME, VI

[7] Sharp gradient estimate and Yau's Liouville theorem for the heat equation on noncompact manifolds [J].

Souplet, Philippe ;

Zhang, Qi S. .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2006, 38 :1045-1053

[8]

Wang Lin Feng, 2010, ACTA MATH SINICA, V53, P643

[9] Gradient estimates for the p-Laplace heat equation under the Ricci flow [J].

Wang, Lin-Feng .

ADVANCES IN GEOMETRY, 2013, 13 (02) :349-368

[10] Elliptic gradient estimates for a weighted heat equation and applications [J].

Wu, Jia-Yong .

MATHEMATISCHE ZEITSCHRIFT, 2015, 280 (1-2) :451-468

← 1 2 →