A remark on energy estimates concerning extremals for Trudinger-Moser inequalities on a disc

被引：10

作者：

Yang, Yunyan ^{[1
]}

机构：

[1] Renmin Univ China, Dept Math, Beijing 100872, Peoples R China

来源：

ARCHIV DER MATHEMATIK | 2018年 / 111卷 / 02期

基金：

美国国家科学基金会;

关键词：

Trudinger-Moser inequality; Extremal function; Energy estimate; Blow-up analysis; SHARP FORM;

D O I：

10.1007/s00013-018-1181-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this short note, we generalized an energy estimate due to Malchiodi-Martinazzi (J Eur Math Soc 16:893-908, 2014) and Mancini-Martinazzi (Calc Var 56:94, 2017). As an application, we used it to reprove existence of extremals for Trudinger-Moser inequalities of Adimurthi-Druet type on the unit disc. Such existence problems in general cases had been considered by Yang (Trans Am Math Soc 359:5761-5776, 2007; J Differ Equ 258:3161-3193, 2015) and Lu-Yang (Discrete Contin Dyn Syst 25:963-979, 2009) by using another method.

引用

页码：215 / 223

页数：9

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