Geodesic
The squares of the laplacian-Dirichlet eigenfunctions are generically linearly independent
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 794-805

Voir la notice de l'article provenant de la source Numdam

corrigé par Erratum of “The squares of the laplacian-Dirichlet eigenfunctions are generically linearly independent”

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 Schrödinger equation.

DOI : 10.1051/cocv/2009014
Classification : 37C20, 47A55, 47A75, 49K20, 49K30, 93B05
Keywords: genericity, laplacian-Dirichlet eigenfunctions, non-resonant spectrum, shape optimization, control 
@article{COCV_2010__16_3_794_0,
     author = {Privat, Yannick and Sigalotti, Mario},
     title = {The squares of the {laplacian-Dirichlet} eigenfunctions are generically linearly independent},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {794--805},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {3},
     year = {2010},
     doi = {10.1051/cocv/2009014},
     mrnumber = {2674637},
     zbl = {1206.35181},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009014/}
}
TY  - JOUR
AU  - Privat, Yannick
AU  - Sigalotti, Mario
TI  - The squares of the laplacian-Dirichlet eigenfunctions are generically linearly independent
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2010
SP  - 794
EP  - 805
VL  - 16
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009014/
DO  - 10.1051/cocv/2009014
LA  - en
ID  - COCV_2010__16_3_794_0
ER  - 
%0 Journal Article
%A Privat, Yannick
%A Sigalotti, Mario
%T The squares of the laplacian-Dirichlet eigenfunctions are generically linearly independent
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2010
%P 794-805
%V 16
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009014/
%R 10.1051/cocv/2009014
%G en
%F COCV_2010__16_3_794_0
Privat, Yannick; Sigalotti, Mario. The squares of the laplacian-Dirichlet eigenfunctions are generically linearly independent. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 3, pp. 794-805. doi: 10.1051/cocv/2009014

Cité par Sources :