%0 Journal Article
%T 加权Laplace在Bakry-Émery Ricci曲率条件下的Li-Yau梯度估计——关于Li-Yau梯度估计的研究
Li-Yau Gradient Estimation of Weighted Laplace under Bakry-Émery Ricci Curvature—Research on Li-Yau Gradient Estimation
%A 唐也
%A 段涵
%J Pure Mathematics
%P 280-286
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.155177
%X 本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,热方程的正解u (x, t)的最优Li-Yau梯度估计。
In this paper, the problem of Li-Yau gradient estimation of weighted Laplace operator under Bakry-Émery Ricci curvature is studied. Bochner formula, weighted Laplace formula and the maximum theorem are used to deal with the Li-Yau gradient problem. The optimal Li-Yau gradient estimation for the positive solution u (x, t) of the heat equation is obtained under the condition of lower bound for weighted Laplace Bakry-Émery Ricci curvature.
%K Li-Yau梯度估计,
%K Bakry-É
%K mery Ricci曲率,
%K Bochner公式,
%K 极大值定理
Li-Yau Gradient Estimation
%K Bakry-É
%K mery Ricci Curvature
%K Bochner Formula
%K Maximum Theorem
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=116186