Fractional Hardy-Sobolev inequalities on half spaces

被引：7

作者：

Musina, Roberta ^{[1
]}

Nazarov, Alexander I. ^{[2
,3
]}

机构：

[1] Univ Udine, Dipartimento Matemat Informat, Via Sci, I-20633100 Udine, Italy

[2] Steklov Inst, St Petersburg Dept, Fontanka 27, St Petersburg 191023, Russia

[3] St Petersburg State Univ, Univ Skii Pr 28, St Petersburg 198504, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2019年 / 178卷

关键词：

Fractional Laplace operators; Sobolev inequality; Hardy inequality; MAZYA INEQUALITY; CONSTANT;

D O I：

10.1016/j.na.2018.07.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the existence of extremals for Hardy-Sobolev inequalities involving the Dirichlet fractional Laplacian (-Delta)(s) of order s is an element of (0, 1) on half-spaces. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：32 / 40

页数：9

共 50 条

[31] Sharp Trace Hardy–Sobolev-Maz’ya Inequalities and the Fractional Laplacian [J].

Stathis Filippas ;

Luisa Moschini ;

Achilles Tertikas .

Archive for Rational Mechanics and Analysis, 2013, 208 :109-161

[32] Cylindrical symmetry of extremals of a Hardy-Sobolev inequality [J].

Mancini G. ;

Sandeep K. .

Annali di Matematica Pura ed Applicata, 2004, 183 (2) :165-172

[33] Hardy-Sobolev equations on compact Riemannian manifolds [J].

Jaber, Hassan .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 103 :39-54

[34] Quasilinear Elliptic Systems Involving Critical Hardy-Sobolev and Sobolev Exponents [J].

Kang, Dongsheng ;

Kang, Yangguang .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2017, 40 (01) :1-17

[35] Sobolev and Hardy-Littlewood-Sobolev inequalities [J].

Dolbeault, Jean ;

Jankowiak, Gaspard .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 257 (06) :1689-1720

[36] Hardy-Sobolev-Maz'ya inequalities for arbitrary domains [J].

Frank, Rupert L. ;

Loss, Michael .

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2012, 97 (01) :39-54

[37] SOME HARDY INEQUALITIES ON HALF SPACES FOR GRUSHIN TYPE OPERATORS [J].

Xiao, Ying-Xiong .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2013, 16 (03) :793-807

[38] The role of the mean curvature in a Hardy-Sobolev trace inequality [J].

Fall, Mouhamed Moustapha ;

Minlend, Ignace Aristide ;

Thiam, El Hadji Abdoulaye .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2015, 22 (05) :1047-1066

[39] On the Sobolev and Hardy constants for the fractional Navier Laplacian [J].

Musina, Roberta ;

Nazarov, Alexander I. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 :123-129

[40] Sobolev, Hardy, Gagliardo–Nirenberg, and Caffarelli–Kohn–Nirenberg-type inequalities for some fractional derivatives [J].

Aidyn Kassymov ;

Michael Ruzhansky ;

Niyaz Tokmagambetov ;

Berikbol T. Torebek .

Banach Journal of Mathematical Analysis, 2021, 15

← 1 2 3 4 5 →