SHARP GRADIENT ESTIMATES FOR A HEAT EQUATION IN RIEMANNIAN MANIFOLDS

被引：21

作者：

Ha Tuan Dung ^{[1
,2
]}

Nguyen Thac Dung ^{[3
,4
]}

机构：

[1] Hanoi Pedag Univ, Fac Math, 2 Xuan Hoa, Xuan Hoa, Vinh Phuc, Vietnam

[2] Natl Tsing Hua Univ, Dept Math, Hsinchu, Taiwan

[3] Hanoi Univ Sci VNU, Fac Math Mech Informat, Hanoi, Vietnam

[4] Thang Long Univ, Thang Long Inst Math & Appl Sci, Hanoi, Vietnam

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2019年 / 147卷 / 12期

关键词：

Ancient solution; heat equation; Liouville theorem; sharp gradient estimate; sublinear growth; THEOREM;

D O I：

10.1090/proc/14645

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove sharp gradient estimates for a positive solution to the heat equation u(t) = Delta u + au log u in complete noncompact Riemannian manifolds. As its application, we show that if u is a positive solution of the equation u(t) = Delta u and log u is of sublinear growth in both spatial and time directions, then u must be constant. This gradient estimate is sharp since it is well known that u(x, t) = e(x+t) satisfying ut = Delta u.

引用

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页码：5329 / 5338

页数：10

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