GENERALIZED HARDY-RELLICH INEQUALITIES IN CRITICAL DIMENSION AND ITS APPLICATIONS

被引：18

作者：

Adimurthi ^{[1
]}

Santra, Sanjiban ^{[2
]}

机构：

[1] TIFR Ctr Applicable Math, Bangalore 560064, Karnataka, India

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS | 2009年 / 11卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Hardy inequalities; biharmonic operator; W-2; W-q(Omega); estimates;

D O I：

10.1142/S0219199709003405

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Hardy-Rellich inequalities for polyharmonic operators in the critical dimension and an analogue in the p-biharmonic case. We also develop some optimal weighted Hardy-Sobolev inequalities in the general case and discuss the related eigenvalue problem. We also prove W-2,W-q(Omega) estimates in the biharmonic case.

引用

页码：367 / 394

页数：28

共 18 条

[1] Optimal Hardy-Rellich inequalities, maximum principle and related eigenvalue problem [J].

Adimurthi ;

Grossi, Massimo ;

Santra, Sanjiban .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 240 (01) :36-83

[2] An improved Hardy-Sobolev inequality in W1,p and its application to Schrodinger operators [J].

Adimurthi ;

Esteban, MJ .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2005, 12 (02) :243-263

[3]

ADIMURTHI, 2006, P ROY SOC EDINB A, V136, P1111

[4]

[Anonymous], 1905, Rend. Circ. Mat. Palermo

[5]

[Anonymous], 1998, Ann Scuola Norm Sup Pisa Cl Sci

[6] A semilinear fourth order elliptic problem with exponential nonlinearity [J].

Arioli, G ;

Gazzola, F ;

Grunau, HC ;

Mitidieri, E .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2005, 36 (04) :1226-1258

[7] On a class of Rellich inequalities [J].

Barbatis, G ;

Tertikas, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2006, 194 (01) :156-172

[8] Existence of positive solutions of some semilinear elliptic equations with singular coefficients [J].

Chaudhuri, N ;

Ramaswamy, M .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2001, 131 :1275-1295

[9]

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

[10] 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

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