THE SQUARES OF THE LAPLACIAN-DIRICHLET EIGENFUNCTIONS ARE GENERICALLY LINEARLY INDEPENDENT (vol 16, pg 794, 2009)

被引：4

作者：

Privat, Yannick ^{[1
]}

Sigalotti, Mario ^{[1
,2
]}

机构：

[1] Nancy Univ, INRIA, CNRS, Inst Elie Cartan Nancy,UMR 7502, F-54506 Vandoeuvre Les Nancy, France

[2] INRIA Nancy Grand Est, Nancy, France

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2010年 / 16卷 / 03期

关键词：

Control; Genericity; Laplacian-Dirichlet eigenfunctions; Non-resonant spectrum; Shape optimization;

D O I：

10.1051/cocv/2009045

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The paper deals with the genericity of domain-dependent spectral properties of the Laplacian-Dirichlet operator. In particular we prove that, generically, the squares of the eigenfunctions form a free family. We also show that the spectrum is generically non-resonant. The results are obtained by applying global perturbations of the domains and exploiting analytic perturbation properties. The work is motivated by two applications: an existence result for the problem of maximizing the rate of exponential decay of a damped membrane and an approximate controllability result for the bilinear Schrodinger equation.

引用

页码：806 / 807

页数：2