Gradient estimates and Harnack inequalities for Yamabe-type parabolic equations on Riemannian manifolds

被引：6

作者：

Ha Tuan Dung ^{[1
]}

机构：

[1] Hanoi Pedag Univ, Dept Math, 2 Nguyen Van Linh Rd, Phuc Yen Dist, Vinh Phuc Provi, Vietnam

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2018年 / 60卷

关键词：

Gradient estimates; Yamabe-type parabolic equations; Harnack inequalities; Liouville-type theorems; Bochner-Weitzenbock; NONCOMPACT MANIFOLDS; SCALAR CURVATURE;

D O I：

10.1016/j.difgeo.2018.05.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (M-n, g) be a complete noncompact n-dimensional Riemannian manifolds. In this paper, we consider the following Yamabe-type parabolic equation u(t) = Delta u + au + bu(alpha) on M-n x [0, infinity). We give a global gradient estimate of Hamilton-type for positive smooth solutions of this equation provided that Ricci curvature bounded from below. As its application, we show a dimension-free Harnack inequality and a Liouville-type theorem for nonlinear elliptic equations. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：39 / 48

页数：10

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