Minimization of the third eigenvalue of the Dirichlet Laplacian

被引：35

作者：

Bucur, D

Henrot, A

机构：

[1] Univ Franche Comte, CNRS, Equipe Math, F-25030 Besancon, France

[2] Univ Henri Poincare, Ecole Mines, Inst Elie Cartan Nancy, UMR CNRS 7502, F-54506 Vandoeuvre Nancy, France

[3] Univ Henri Poincare, INRIA, F-54506 Vandoeuvre Nancy, France

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2000年 / 456卷 / 1996期

关键词：

Laplace operator; shape optimization; third eigenvalue;

D O I：

10.1098/rspa.2000.0546

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this paper, we prove the existence of a domain which minimizes the third Dirichlet eigenvalue lambda(3) of the Laplacian (-Delta) in the family of domains of R-N of given volume. Some remarks are made on the existence of a minimizer for lambda(k), k greater than or equal to 4 in the same family, and for a class of functionals depending on (lambda(1):lambda(2)).

引用

页码：985 / 996

页数：12

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