EQUIVALENCE OF SHARP TRUDINGER-MOSER-ADAMS INEQUALITIES

被引：10

作者：

Nguyen Lam ^{[1
]}

机构：

[1] Univ British Columbia, Pacific Inst Math Sci, Dept Math, Vancouver, BC V6T 1Z4, Canada

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2017年 / 16卷 / 03期

关键词：

Optimizers; best constants; Trudinger-Moser inequalities; Adams inequalities; Lions type; EXTREMAL-FUNCTIONS; UNBOUNDED-DOMAINS;

D O I：

10.3934/cpaa.2017047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Improved Trudinger-Moser-Adams type inequalities in the spirit of Lions were recently studied in [21]. The main purpose of this paper is to prove the equivalence of these versions of the Trudinger-Moser-Adams type inequalities and to set up the relations of these Trudinger-Moser-Adams best constants. Moreover, using these identities, we will investigate the existence and nonexistence of the optimizers for some Trudinger-Moser-Adams type inequalities.

引用

页码：973 / 997

页数：25

共 36 条

[1] Trudinger type inequalities in RN and their best exponents
Adachi, S
Tanaka, K
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (07) : 2051 - 2057
[2] A SHARP INEQUALITY OF MOSER,J. FOR HIGHER-ORDER DERIVATIVES
ADAMS, DR
[J]. ANNALS OF MATHEMATICS, 1988, 128 (02) : 385 - 398
[3] An Interpolation of Hardy Inequality and Trudinger-Moser Inequality in RN and Its Applications
Adimurthi
Yang, Yunyan
[J]. INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2010, 2010 (13) : 2394 - 2426
[4] A singular Moser-Trudinger embedding and its applications
Adimurthi
Sandeep, K.
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2007, 13 (5-6): : 585 - 603
[5] [Anonymous], PREPRINT
[6] CARLESON L, 1986, B SCI MATH, V110, P113
[7] Equivalent Moser type inequalities in R2 and the zero mass case
Cassani, D.
Sani, F.
Tarsi, C.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 267 (11) : 4236 - 4263
[8] Singular Moser-Trudinger inequality on simply connected domains
Csato, Gyula
Roy, Prosenjit
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2016, 41 (05) : 838 - 847
[9] Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions
Csato, Gyula
Roy, Prosenjit
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2015, 54 (02) : 2341 - 2366
[10] do J. M., 1997, Abstr. Appl. Anal., V2, P301

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