Trudinger-Moser inequality with remainder terms

被引：68

作者：

Tintarev, Cyril ^{[1
]}

机构：

[1] Uppsala Univ, Dept Math, S-75106 Uppsala, Sweden

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 01期

基金：

瑞典研究理事会;

关键词：

Trudinger-Moser inequality; Borderline Sobolev imbeddings; Singular elliptic operators; Remainder terms; Spectral gap; Virtual bound state; Hardy-Sobolev-Mazya inequality;

D O I：

10.1016/j.jfa.2013.09.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper gives the following improvement of the Trudinger-Moser inequality: [GRAPHICS] related to the Hardy-Sobolev-Mazya inequality in higher dimensions. We show (0.1) with psi(u) = integral(Omega) V(x)u(2) dx for a class of V > 0 that includes [GRAPHICS] which refines two previously known cases of (0.1) proved by Adimurthi and Druet [2] and by Wang and Ye [23]. In addition, we verify (0.1) for psi(u) = lambda parallel to u parallel to(2)(P), as well as give an analogous improvement for the Onofri-Beckner inequality for the unit disk (Beckner [6]). (C) 2013 The Author. Published by Elsevier Inc. All rights reserved.

引用

页码：55 / 66

页数：12

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