MOSER-TRUDINGER INEQUALITY ON CONFORMAL DISCS

被引：64

作者：

Mancini, G. ^{[1
]}

Sandeep, K. ^{[2
]}

机构：

[1] Univ Roma Tre, Dipartimento Matemat, I-00146 Rome, Italy

[2] TIFR Ctr Applicable Math, Bangalore 560065, Karnataka, India

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2010年 / 12卷 / 06期

关键词：

Moser-Trudinger inequality; conformal disc; SEMILINEAR ELLIPTIC EQUATION; NONPOSITIVE CURVATURE; SOBOLEV INEQUALITIES; COMPLETE METRICS; EXPONENT;

D O I：

10.1142/S0219199710004111

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a sharp Moser-Trudinger inequality holds true on a conformal disc if and only if the metric is bounded from above by the Poincare metric. We also derive necessary and sufficient conditions for the validity of a sharp Moser-Trudinger inequality on a simply connected domain in R-2.

引用

页码：1055 / 1068

页数：14

共 24 条

[1] Trudinger type inequalities in RN and their best exponents [J].

Adachi, S ;

Tanaka, K .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 128 (07) :2051-2057

[2] On a version of Trudinger-Moser inequality with Mobius shift invariance [J].

Adimurthi ;

Tintarev, Kyril .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2010, 39 (1-2) :203-212

[3]

[Anonymous], 1969, Transl. Math. Monographs

[4]

AVILES P, 1985, J DIFFER GEOM, V21, P269

[5]

BAERNSTEIN A, 1994, SYM MATH, V35, P47

[6] SHARP SOBOLEV INEQUALITIES ON THE SPHERE AND THE MOSER-TRUDINGER INEQUALITY [J].

BECKNER, W .

ANNALS OF MATHEMATICS, 1993, 138 (01) :213-242

[7] COMPLETE METRICS CONFORMAL TO THE HYPERBOLIC DISK [J].

BLAND, J ;

KALKA, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 97 (01) :128-132

[8]

BRANSON TP, ARXIV07123905V2MATHA

[9] NONTRIVIAL SOLUTION OF SEMILINEAR ELLIPTIC EQUATION WITH CRITICAL EXPONENT IN R2 [J].

CAO, DM .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1992, 17 (3-4) :407-435

[10]

Cheng KS, 2000, CALC VAR PARTIAL DIF, V11, P203, DOI 10.1007/s005260000037

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