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 Schr\"odinger equation. 
Yannick Privat (IECN, Inria Lorraine / Iecn / Mmas), Mario Sigalotti   (IECN, Inria Lorraine / Iecn / Mmas)