Gradient estimates for some evolution equations on complete smooth metric measure spaces

被引：1

作者：

Nguyen Thac Dung ^{[1
,2
]}

Kieu Thi Thuy Linh ^{[3
]}

Ninh Van Thu ^{[1
]}

机构：

[1] Hanoi Univ Sci VNU, Fac Math Mech Informat, 334 Nguyen Trai Rd, Hanoi, Vietnam

[2] THANG Long Univ, Thang Long Inst Math & Appl Sci TIMAS, Hanoi, Vietnam

[3] Natl Univ Civil Engn, Fac Informat Technol, 55 Giai Phong Rd, Hanoi, Vietnam

来源：

PUBLICATIONES MATHEMATICAE-DEBRECEN | 2020年 / 96卷 / 1-2期

关键词：

gradient estimates; Bakry-Emery curvature; complete smooth metric measure space; Harnack-type inequalities; Liouville-type theorems; NONLINEAR PARABOLIC EQUATION; HEAT-EQUATION; THEOREM; EXTENSION; KERNEL;

D O I：

10.5486/PMD.2020.8248

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the following general evolution equation u(t) = Delta(f)u + aulog(alpha)u + bu on a smooth metric measure space (M-n, g, e(-f)dv). We give a local gradient estimate of Souplet-Zhang type for positive smooth solutions of this equation provided that the Bakry-Emery curvature is bounded from below. When f is constant, we investigate the general evolution equation on compact Riemannian manifolds with nonconvex boundary satisfying an interior rolling R-ball condition. We show a gradient estimate of Hamilton type on such manifolds.

引用

页码：1 / 21

页数：21

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