Elliptic gradient estimates for a nonlinear f-heat equation on weighted manifolds with evolving metrics and potentials

被引：8

作者：

Abolarinwa, Abimbola ^{[1
]}

Taheri, Ali ^{[2
]}

机构：

[1] Univ Lagos, Dept Math, Akoka Yaba, Lagos State, Nigeria

[2] Univ Sussex, Sch Math & Phys Sci, Brighton, E Sussex, England

来源：

CHAOS SOLITONS & FRACTALS | 2021年 / 142卷

关键词：

Gradient estimates; Perelman-Ricci flow; Weighted manifolds; Heat kernel; Logarithmic Sobolev inequalities; Maximum principle;

D O I：

10.1016/j.chaos.2020.110329

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop local elliptic gradient estimates for a basic nonlinear f-heat equation with a logarithmic power nonlinearity and establish pointwise upper bounds on the weighted heat kernel, all in the context of weighted manifolds, where the metric and potential evolve under a Perelman-Ricci type flow. For the heat bounds use is made of entropy monotonicity arguments and ultracontractivity estimates with the bounds expressed in terms of the optimal constant in the logarithmic Sobolev inequality. Some interesting consequences of these estimates are presented and discussed. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：14

共 36 条

[1] Elliptic gradient estimates and Liouville theorems for a weighted nonlinear parabolic equation [J].