Blow-up analysis concerning singular Trudinger-Moser inequalities in dimension two

被引：67
|
作者：
Yang, Yunyan [1 ]
Zhu, Xiaobao [1 ]
机构：
[1] Renmin Univ China, Dept Math, Beijing 100872, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2017年 / 272卷 / 08期
基金：
美国国家科学基金会;
关键词：
Singular Trudinger-Moser inequality; Blow-up analysis; L-P NORM; SHARP FORM; EXTREMAL-FUNCTIONS; EXISTENCE; CONSTANT;
D O I：
10.1016/j.jfa.2016.12.028
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we derive a sharp version of the singular Trudinger Moser inequality, which was originally established by Adimurthi and Sandeep [2]. Moreover, extremal functions for those singular Trudinger Moser inequalities are also obtained. Our method is the blow-up analysis. Compared with our previous work ([32]), the essential difficulty caused by the presence of singularity is how to analyse the asymptotic behavior of certain maximizing sequence near the blow-up point. We overcome this difficulty by combining two different classification theorems of Chen and Li [6,7] to get the desired bubble.(C) 2017 Elsevier Inc. All rights reserved.
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页码：3347 / 3374
页数：28
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