Moser-Trudinger inequalities: from local to global

被引：0

作者：

Fontana, Luigi ^{[1
]}

Morpurgo, Carlo ^{[2
]}

Qin, Liuyu ^{[3
]}

机构：

[1] Univ Milano Bicocca, Dipartimento Matemat & Applicazioni, Milan, Italy

[2] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[3] Hunan Univ Finance & Econ, Dept Math & Stat, Changsha, Hunan, Peoples R China

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2025年 / 204卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Moser-Trudinger inequality; Poincare' inequality; Riemannian manifolds; UNBOUNDED-DOMAINS; RIEMANNIAN-MANIFOLDS; EIGENVALUE;

D O I：

10.1007/s10231-024-01481-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a general complete Riemannian manifold M, we introduce the concept of "local Moser-Trudinger inequality on W1,n(M)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$W<^>{1,n}(M)$$\end{document}". We show how the validity of the Moser-Trudinger inequality can be extended from a local to a global scale under additional assumptions: either by assuming the validity of the Poincar & eacute; inequality, or by imposing a stronger norm condition. We apply these results to Hadamard manifolds. The technique is general enough to be applicable also in sub-Riemannian settings, such as the Heisenberg group.

引用

页码：231 / 243

页数：13