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Pure Mathematics 2025
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
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Abstract:
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.
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