A SHARP TRUDINGER-MOSER TYPE INEQUALITY IN R2

被引：53
作者：
de Souza, Manasses [1 ]
do O, Joao Marcos [2 ]
机构：
[1] Univ Fed Pernambuco, Dept Matemat, BR-50740540 Recife, PE, Brazil
[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2014年 / 366卷 / 09期
关键词：
Trudinger-Moser inequality; blow-up analysis; extremal function; EXTREMAL-FUNCTIONS; UNBOUNDED-DOMAINS; EXISTENCE; EQUATIONS; CONSTANT;
D O I：
10.1090/S0002-9947-2014-05811-X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we establish a sharp Trudinger-Moser type inequality for a class of Schrodinger operators in R-2. We obtain a result related to the compactness of the embedding of a subspace of W-1,W-2(R-2) into the Orlicz space L-phi(R-2) determined by phi(t) = E-beta t2-1. Our result is similar to one obtained by Adimurthi and Druet for smooth bounded domains in R-2, which is closely related to a compactness result proved by Lions. Furthermore, similarly to what has been done by Carleson and Chang, we prove the existence of an extremal function for this Trudinger-Moser inequality by performing a blow-up analysis. Trudinger-Moser type inequalities have a wide variety of applications to the study of nonlinear elliptic partial differential equations involving the limiting case of Sobolev inequalities and have received considerable attention in recent years.
引用
收藏
页码：4513 / 4549
页数：37
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