Gradient estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition

被引：0
|
作者：
Olive, Xavier Ramos [1 ]
Seto, Shoo [2 ]
机构：
[1] Coll Holy Cross, Dept Math & Comp Sci, Swords Hall 326,1 Coll St, Worcester, MA 01610 USA
[2] Calif State Univ, Dept Math, Fullerton, CA 92831 USA
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2025年 / 98卷
关键词：
Gradient estimate; Integral Ricci curvature; Bakry-& Eacute; mery-Ricci tensor; COMPARISON GEOMETRY; COMPACT MANIFOLDS; CURVATURE; BOUNDS; KERNEL;
D O I：
10.1016/j.difgeo.2024.102222
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a global gradient estimate to positive solutions of the nonlinear parabolic equation ut = Delta fu + au ln(u) + bu under an integral Bakry-& Eacute;mery Ricci condition on compact weighted manifolds. The elliptic version of the equation arises in the study of gradient Ricci solitons and in this paper we consider the parabolic version. (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
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