A SHARP TRUDINGER-MOSER TYPE INEQUALITY IN R2

被引：51

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

页码：4513 / 4549

页数：37

共 37 条

[21] Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
Li, YX
[J]. SCIENCE IN CHINA SERIES A-MATHEMATICS, 2005, 48 (05): : 618 - 648
[22] Extremal functions for Moser's inequality
Lin, KC
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (07) : 2663 - 2671
[23] Lions P-L., 1985, Rev. Mat. Iberoamericana, V1, P145, DOI [DOI 10.4171/RMI/6, 10.4171/rmi/6]
[24] SHARP CONSTANT AND EXTREMAL FUNCTION FOR THE IMPROVED MOSER-TRUDINGER INEQUALITY INVOLVING Lp NORM IN TWO DIMENSION
Lu, Guozhen
Yang, Yunyan
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (03) : 963 - 979
[25] Marcos do Joao, 2008, J MATH ANAL APPL, V345, P286, DOI [10.1016/j.jmaa.2008.03.074, DOI 10.1016/J.JMAA.2008.03.074.]
[26] SHARP FORM OF AN INEQUALITY BY N TRUDINGER
MOSER, J
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1971, 20 (11) : 1077 - &
[27] On semilinear neumann problems with critical growth for the n-Laplacian
Panda, R
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (08) : 1347 - 1366
[28] Pohozaev S.I., 1965, P TECH SCI C ADV SCI, P158
[29] Polya G., 1951, Ann. Math. Stud., V27
[30] ON A CLASS OF NONLINEAR SCHRODINGER-EQUATIONS
RABINOWITZ, PH
[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1992, 43 (02): : 270 - 291

← 1 2 3 4 →