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

  title={The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent Yannick Privat},
  author={Yannick Privat and Mario Sigalotti},
The paper deals with the genericity of domain-dependent sp ectral properties of the Laplacian-Dirichlet operator. In partic ular 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 o btained by applying global perturbations of the domains and exploiting analyti c perturbation properties. The work is motivated by two applications: an existe nce result for the problem of maximizing the rate… CONTINUE READING
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