The eigenvalues of the Laplacian with Dirichlet boundary condition in are almost never minimized by disks

被引：0

作者：

Berger, Amandine ^{[1
,2
]}

机构：

[1] Univ Neuchatel, Math Inst, Rue Emile Argand 11, CH-2000 Neuchatel, Switzerland

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

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2015年 / 47卷 / 03期

基金：

瑞士国家科学基金会;

关键词：

Eigenvalues; Laplacian; Dirichlet; Minimization; Disks; OPTIMIZATION;

D O I：

10.1007/s10455-014-9446-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Minimization of the Dirichlet eigenvalues of the Laplacian among sets of prescribed measure is a standard problem in shape optimization. The main result of this paper is that in the Euclidean plane, apart from the first four, no Dirichlet eigenvalue can be minimized by disks or disjoint unions of disks.

引用

页码：285 / 304

页数：20

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