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

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

Abstract

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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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

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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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

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