On the first eigenvalue of a fourth order Steklov problem

被引：38

作者：

Bucur, Dorin ^{[2
]}

Ferrero, Alberto ^{[3
]}

Gazzola, Filippo ^{[1
]}

机构：

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

[2] Univ Savoie, CNRS, UMR 5127, Math Lab, F-73376 Le Bourget Du Lac, France

[3] Univ Milan, Dipartimento Matemat & Applicaz, I-20125 Milan, Italy

来源：

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 35卷 / 01期

关键词：

COUPLED EQUATION APPROACH; BIHARMONIC EQUATION; BOUNDARY-CONDITIONS; NUMERICAL SOLUTION; FINITE DIFFERENCES; DOMAINS; POSITIVITY; OPERATOR;

D O I：

10.1007/s00526-008-0199-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove some results about the first Steklov eigenvalue d (1) of the biharmonic operator in bounded domains. Firstly, we show that Fichera's principle of duality (Fichera in Atti Accad Naz Lincei 19:411-418, 1955) may be extended to a wide class of nonsmooth domains. Next, we study the optimization of d (1) for varying domains: we disprove a long-standing conjecture, we show some new and unexpected features and we suggest some challenging problems. Finally, we prove several properties of the ball.

引用

页码：103 / 131

页数：29

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