%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