Hardy-Rellich inequalities with boundary remainder terms and applications

被引：24

作者：

Berchio, Elvise ^{[1
]}

Cassani, Daniele ^{[1
,2
]}

Gazzola, Filippo ^{[1
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

[2] Univ Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

MANUSCRIPTA MATHEMATICA | 2010年 / 131卷 / 3-4期

关键词：

SUPERCRITICAL BIHARMONIC-EQUATIONS; 4TH-ORDER ELLIPTIC PROBLEM; POSITIVE SOLUTIONS; CONSTANTS; EIGENVALUE; OPERATOR;

D O I：

10.1007/s00229-009-0328-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a family of Hardy-Rellich inequalities with optimal constants and additional boundary terms. These inequalities are used to study the behavior of extremal solutions to biharmonic Gelfand-type equations under Steklov boundary conditions.

引用

页码：427 / 458

页数：32

共 46 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]

[Anonymous], 1997, Rev. Mat. Univ. Complut. Madrid

[3]

[Anonymous], 1980, Commun. Partial Differ. Equ

[4]

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

[5]

[Anonymous], 2002, Modeling MEMS and NEMS

[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] Entire solutions for a semilinear fourth order elliptic problem with exponential nonlinearity [J].

Arioli, Gianni ;

Gazzola, Filippo ;

Grunau, Hans-Christoph .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2006, 230 (02) :743-770

[8]

B?nilan P., 1995, ANN SCUOLA NORM-SCI, V22, P241

[9] Best constants for higher-order Rellich inequalities in Lp (Ω) [J].

Barbatis, G. .

MATHEMATISCHE ZEITSCHRIFT, 2007, 255 (04) :877-896

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

Barbatis, G ;

Tertikas, A .

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

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