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.
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页码：55 / 66
页数：12
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