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.
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收藏
页码：427 / 458
页数：32
相关论文
共 46 条
[41]  
MITIDIERI E, 2001, P STEKLOV I MATH, V234, P375
[42]  
MORADIFAM A, SINGULAR EXTREMAL SO
[43]  
Rellich F., 1956, P INT C MATH 1954 AM, VIII, P243
[44]   Best constants in the Hardy-Rellich inequalities and related improvements [J].
Tertikas, A. ;
Zographopoulos, N. B. .
ADVANCES IN MATHEMATICS, 2007, 209 (02) :407-459
[45]  
van der Vorst R.C.A.M., 1993, Differential Integral Equations, V6, P259
[46]   REGULARITY OF THE EXTREMAL SOLUTION FOR A BIHARMONIC PROBLEM WITH GENERAL NONLINEARITY [J].
Warnault, Guillaume .
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2009, 8 (05) :1709-1723
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