QUALITATIVE AND NUMERICAL ANALYSIS OF A SPECTRAL PROBLEM WITH PERIMETER CONSTRAINT

被引：18

作者：

Bogosel, Beniamin ^{[1
]}

Oudet, Edouard ^{[2
]}

机构：

[1] Univ Savoie, Math Lab, F-73376 Le Bourget Du Lac, France

[2] Univ Grenoble 1, Lab Jean Kuntzmann, F-38041 Grenoble 9, France

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2016年 / 54卷 / 01期

关键词：

shape optimization; eigenvalues; gamma convergence; optimality conditions; DIRICHLET; MINIMIZATION; EIGENVALUES; PARTITIONS; IMMERSIONS; REGULARITY;

D O I：

10.1137/140999530

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We consider the problem of optimizing the kth eigenvalue of the Dirichlet Laplace operator under perimeter constraint. We provide a new method based on a Gamma-convergence result for approximating the corresponding optimal shapes. We also give new optimality conditions in the case of multiple eigenvalues. We deduce from previous conditions the fact that optimal shapes never contain flat parts in their boundaries.

引用

页码：317 / 340

页数：24

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