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,...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.展开更多
文摘本文研究了在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.
