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

被引：0

作者：

Wu, Wenjing ^{[1
]}

机构：

[1] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 248卷

基金：

中国国家自然科学基金;

关键词：

Talenti comparison; Reverse H & ouml; lder inequality; p-laplacian; METRIC-MEASURE-SPACES; RICCI CURVATURE; ISOPERIMETRIC-INEQUALITIES; RIEMANNIAN-MANIFOLDS; LIPSCHITZ FUNCTIONS; EIGENFUNCTION; EIGENVALUES; SHARP;

D O I：

10.1016/j.na.2024.113631

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, K, N ) space with K > 0 and N E (1 infinity). 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 H & ouml;lder inequality for first eigenfunctions of the p-Laplacian and a related quantitative stability result.

引用

页数：29

共 11 条

[1] A Talenti-type comparison theorem for RCD(K, N) spaces and applications
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[2] A Talenti-type comparison theorem for RCD(K,N)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\,\mathrm{RCD}\,}}(K,N)$$\end{document} spaces and applications
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