TRUDINGER-MOSER EMBEDDINGS ON WEIGHTED SOBOLEV SPACES ON UNBOUNDED DOMAINS

被引：0

作者：

Do, Joao Marcos ^{[1
]}

Lu, Guozhen ^{[2
]}

Ponciano, Raoni Cabreal ^{[1
]}

机构：

[1] Univ Fed Paraiba, BR-58051900 Joao Pessoa, PB, Brazil

[2] Univ Connecticut, Storrs, CT 06269 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2025年 / 45卷 / 02期

关键词：

Sobolev spaces; Trudinger-Moser type inequality; Differential Equa tions; Fractional Dimensions; Maximizers; EXTREMAL-FUNCTIONS; INEQUALITIES; EXISTENCE; EQUATIONS; COMPACTNESS; GROWTH;

D O I：

10.3934/dcds.2024103

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish embeddings on a class of Sobolev spaces with potential weights on unbounded domains. Our results provide embeddings into weighted Lebesgue spaces L q theta with radial power weights and establish the existence and non-existence of the maximizers for their Trudinger-Moser type inequalities. We also sharpen the maximal integrability by "removing" necessary terms from the exponential series while maintaining the continuity of the embedding.

引用

页码：557 / 584

页数：28

共 48 条

[1] On a weighted Trudinger-Moser inequality in RN [J].

Abreu, Emerson ;

Fernandes Jr, Leandro G. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (04) :3089-3118

[2] 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

[3] Sobolev and isoperimetric inequalities with monomial weights [J].

Cabre, Xavier ;

Ros-Oton, Xavier .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (11) :4312-4336

[4] 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

[5] Existence of extremals for Trudinger-Moser inequalities involved with a trapping potential [J].

Chen, Lu ;

Lu, Guozhen ;

Zhu, Maochun .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2023, 62 (05)

[6] Existence and nonexistence of extremals for critical Adams inequalities in R4 and Trudinger-Moser inequalities in R2 [J].

Chen, Lu ;

Lu, Guozhen ;

Zhu, Maochun .

ADVANCES IN MATHEMATICS, 2020, 368

[7]

Clement P., 1996, TOPOL METHOD NONL AN, V7, P133, DOI [10.12775/TMNA.1996.006, DOI 10.12775/TMNA.1996.006]

[8] Best constants for Moser-Trudinger inequalities on the Heisenberg group [J].

Cohn, WS ;

Lu, GZ .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2001, 50 (04) :1567-1591

[9] On an inequality by N. Trudinger and J. Moser and related elliptic equations [J].

de Figueiredo, DG ;

Do O, JM ;

Ruf, B .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2002, 55 (02) :135-152

[10] ELLIPTIC EQUATIONS AND SYSTEMS WITH CRITICAL TRUDINGER-MOSER NONLINEARITIES [J].

de Figueiredo, Djairo G. ;

do O, Joao Marcos ;

Ruf, Bernhard .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 30 (02) :455-476

← 1 2 3 4 5 →