An analytical proof of Hardy-like inequalities related to the Dirac operator

被引：33

作者：

Dolbeault, J ^{[1
]}

Esteban, MJ

Loss, M

Vega, L

机构：

[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

[2] Georgia Tech, Sch Math, Atlanta, GA 30332 USA

[3] Univ Basque Country, Dept Matemat, Fac Ciencias, E-48080 Bilbao, Spain

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2004年 / 216卷 / 01期

基金：

美国国家科学基金会;

关键词：

Hardy inequality; Dirac operator; optimal constants; Dirac-Coulomb Hamiltonian; relativistic hydrogen atom;

D O I：

10.1016/j.jfa.2003.09.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：1 / 21

页数：21

共 19 条

[1]

Adimurthi, 2002, P ROY SOC EDINB A, V132, P1021

[2] Hardy-Sobolev inequality in H1(Ω) and its applications [J].

Adimurthi .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2002, 4 (03) :409-434

[3] An improved Hardy-Sobolev inequality and its application [J].

Adimurthi ;

Chaudhuri, N ;

Ramaswamy, M .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (02) :489-505

[4]

ADIMURTHI MJ, IN PRESS IMPROVED HA

[5]

Barbatis G, 2003, INDIANA U MATH J, V52, P171

[6]

BARBATIS G, 2001, UNIFIED APPROACH IMP

[7]

Brezis H., 1997, Rev. Mat. Univ. Complut. Madrid, V10, P443

[8]

Dolbeault J, 2000, J FUNCT ANAL, V174, P208, DOI 10.1006/jfan.2000.3542

[9] Variational characterization for eigenvalues of Dirac operators [J].

Dolbeault, J ;

Esteban, MJ ;

Séré, E .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2000, 10 (04) :321-347

[10]

Esteban M., 1997, CRM P LECT NOTES, V12

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