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Hamilton inequality for unbounded Laplacians on graphs
Differential Geometry and its Applications ( IF 0.5 ) Pub Date : 2021-03-30 , DOI: 10.1016/j.difgeo.2021.101758 Yongtao Liu
中文翻译:
图上无界拉普拉斯算子的汉密尔顿不等式
更新日期:2021-03-30
Differential Geometry and its Applications ( IF 0.5 ) Pub Date : 2021-03-30 , DOI: 10.1016/j.difgeo.2021.101758 Yongtao Liu
In this paper, we study Hamilton inequality for unbounded Laplacians on weighted graphs satisfying for some . This is a generalization of the main result in [8] for bounded Laplacians. For this purpose, we assume a non-degenerated measure and make some modifications to the solutions of the heat equation. As an application of Hamilton inequality, we derive a type of Harnack inequality which compares the heat of two different vertices at the same time.
中文翻译:
图上无界拉普拉斯算子的汉密尔顿不等式
在本文中,我们在满足以下条件的加权图上研究无界拉普拉斯算子的汉密尔顿不等式 对于一些 。这是有界拉普拉斯算子在[8]中主要结果的概括。为此,我们假设采用非退化措施,并对热方程的解进行一些修改。作为汉密尔顿不等式的一种应用,我们导出了一种哈纳克不等式,它同时比较了两个不同顶点的热量。