GRADIENT ESTIMATES FOR A NONLINEAR PARABOLIC EQUATION WITH DIRICHLET BOUNDARY CONDITION

被引：0

作者：

Fu, Xuenan ^{[1
]}

Wu, Jia-Yong ^{[1
]}

机构：

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

KODAI MATHEMATICAL JOURNAL | 2022年 / 45卷 / 01期

关键词：

Smooth metric measure space; Bakry-Emery Ricci curvature; manifold with boundary; gradient estimate; Liouville theorem; METRIC-MEASURE-SPACES; RICCI CURVATURE; EIGENVALUE ESTIMATE; HEAT-EQUATION; MANIFOLDS; RIGIDITY; KERNEL;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove Souplet-Zhang type gradient estimates for a nonlinear parabolic equation on smooth metric measure spaces with the compact boundary under the Dirichlet boundary condition when the Bakry-Emery Ricci tensor and the weighted mean curvature are both bounded below. As an application, we obtain a new Liouville type result for some space-time functions on such smooth metric measure spaces. These results generalize previous linear equations to a nonlinear case.

引用

页码：96 / 109

页数：14

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