On the Sobolev and Hardy constants for the fractional Navier Laplacian

被引：13

作者：

Musina, Roberta ^{[1
]}

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

机构：

[1] Univ Udine, Dipartimento Matemat & Informat, I-33100 Udine, Italy

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

[3] St Petersburg State Univ, St Petersburg 198504, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 121卷

关键词：

Fractional Laplacians; Sobolev inequality; Hardy inequality; EXTENSION PROBLEM; INEQUALITIES;

D O I：

10.1016/j.na.2014.09.021

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the coincidence of the Sobolev and Hardy constants relative to the "Dirichlet" and "Navier" fractional Laplacians of any real order m epsilon (0, n/2) over bounded domains in R-n. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：123 / 129

页数：7

共 21 条

[1]

[Anonymous], 1993, Differ. Integral Equ.

[2]

[Anonymous], ARXIV14083568

[3] Positive solutions of nonlinear problems involving the square root of the Laplacian [J].

Cabre, Xavier ;

Tan, Jinggang .

ADVANCES IN MATHEMATICS, 2010, 224 (05) :2052-2093

[4] An extension problem related to the fractional Laplacian [J].

Caffarelli, Luis ;

Silvestre, Luis .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2007, 32 (7-9) :1245-1260

[5] Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations [J].

Capella, Antonio ;

Davila, Juan ;

Dupaigne, Louis ;

Sire, Yannick .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (08) :1353-1384

[6] Best constants for Sobolev inequalities for higher order fractional derivatives [J].

Cotsiolis, A ;

Tavoularis, NK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 295 (01) :225-236

[7]

Davies EB, 1998, MATH Z, V227, P511, DOI 10.1007/PL00004389

[8] Hardy inequalities with optimal constants and remainder terms [J].

Gazzola, F ;

Grunau, HC ;

Mitidieri, E .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 356 (06) :2149-2168

[9] Optimal Sobolev and Hardy-Rellich constants under Navier boundary conditions [J].

Gazzola, Filippo ;

Grunau, Hans-Christoph ;

Sweers, Guido .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2010, 189 (03) :475-486

[10] Sharp Sobolev inequalities in critical dimensions [J].

Ge, YX .

MICHIGAN MATHEMATICAL JOURNAL, 2003, 51 (01) :27-45

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