The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent
Yannick Privat, Mario Sigalotti (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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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...