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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2010

The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent

Résumé

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.
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Dates et versions

hal-00322301 , version 1 (17-09-2008)
hal-00322301 , version 2 (19-05-2009)
hal-00322301 , version 3 (11-09-2009)

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Yannick Privat, Mario Sigalotti. The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent. ESAIM: Control, Optimisation and Calculus of Variations, 2010, 16 (3), pp.794-805. ⟨10.1051/cocv/2009014⟩. ⟨hal-00322301v3⟩
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