图上具有椭圆性条件的无界拉普拉斯的梯度估计

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-10-24 DOI:10.1016/j.jmaa.2024.128996

Yong Lin , Shuang Liu

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引用次数: 0

摘要

在本文中，我们证明了满足椭圆性条件的无界图拉普拉斯的各种梯度估计。与无界拉普拉斯的常见假设（即完备性和非退化度量）不同，椭圆性条件是纯局部的，易于在图上验证。首先，我们建立了一个等效的半群性质，即指数曲率-维度不等式的梯度估计，它是曲率-维度不等式的一种修正，可视为图上的曲率概念。此外，我们还利用半群方法证明了椭圆性条件下图上无界拉普拉斯的李-尤不等式和汉密尔顿不等式。

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Gradient estimates for unbounded Laplacians with ellipticity condition on graphs

In this article, we prove various gradient estimates for unbounded graph Laplacians which satisfy the ellipticity condition. Unlike common assumptions for unbounded Laplacians, i.e. completeness and non-degenerate measure, the ellipticity condition is purely local that is easy to verify on a graph. First, we establish an equivalent semigroup property, namely the gradient estimate of exponential curvature-dimension inequality, which is a modification of the curvature-dimension inequality and can be viewed as a notion of curvature on graphs. Additionally, we use the semigroup method to prove the Li-Yau inequalities and the Hamilton inequality for unbounded Laplacians on graphs with the ellipticity condition.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.