RCD(K,N)空间上 p-拉普拉斯的塔伦蒂型比较定理及其一些应用

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-02 DOI:10.1016/j.na.2024.113631

Wenjing Wu

引用次数: 0

摘要

本文证明了在K>0和N∈(1,∞)的归一化RCD(K,N)空间的开放子集上具有迪里希特边界条件的p-拉普拉奇的塔伦蒂型比较定理。所得到的塔伦提型比较定理对于测量的格罗莫夫-豪斯多夫拓扑学来说是尖锐的、刚性的和稳定的。作为塔伦提式比较定理的一个应用，我们为 p-拉普拉奇的第一特征函数建立了一个尖锐、刚性的反向赫尔德不等式和一个相关的定量稳定性结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Talenti-type comparison theorem for the p-Laplacian on RCD(K,N) spaces and some applications

In this paper, we prove a Talenti-type comparison theorem for the $p$ -Laplacian with Dirichlet boundary conditions on open subsets of a normalized $RCD (K, N)$ space with $K > 0$ and $N \in (1, \infty)$ . The obtained Talenti-type comparison theorem is sharp, rigid and stable with respect to measured Gromov–Hausdorff topology. As an application of such Talenti-type comparison, we establish a sharp and rigid reverse Hölder inequality for first eigenfunctions of the $p$ -Laplacian and a related quantitative stability result.

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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.