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

@inproceedings{Privat2008TheSO,
  title={The squares of the Laplacian-Dirichlet eigenfunctions are generically linearly independent Yannick Privat},
  author={Yannick Privat and Mario Sigalotti},
  year={2008}
}
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
Highly Cited
This paper has 23 citations. REVIEW CITATIONS

References

Publications referenced by this paper.
Showing 1-10 of 38 references

Generic simplicity of the eigenvalues of the Stokes system in two space dimensions. Adv. Differential Equations

  • Jaime H. Ortega, Enrique Zuazua
  • 2001
Highly Influential
12 Excerpts

A generic uniq ueness result for the Stokes system and its control theoretical consequences

  • Jacques-Louis Lions, Enrique Zuazua
  • ofLecture Notes in Pure and Appl. Math. ,
  • 1996
Highly Influential
12 Excerpts

Sturm-Liouville eigenval ue problems in which the squares of the eigenfunctions are linearly dependent

  • T. J. Mahar, B. E. Willner
  • Comm. Pure Appl. Math
  • 1980
Highly Influential
3 Excerpts

Controllability of the discrete - spectrum Schrödinger equation driven by an external field

  • J.-M. Coron Chitour, M. Garavello
  • Ann . Inst . H . Poincaré Anal . Non Linéaire
  • 2009

Controllability of the discrete-spectrum Schrödinger equation driven by an exte rnal field.Annales de l’Institut Henri Poincaré, analyse non linéaire

  • Thomas Chambrion, Paolo Mason, Mario Sigalotti, Ugo Boscain
  • 2009
3 Excerpts

Spectral controllability for 2 D and 3 D linear Schrödinger equations

  • P. Mason Chambrion, M. Sigalotti, U. Boscain
  • J . Funct . Anal .
  • 2009

Controllability o n the group of diffeomorphisms

  • Andrei Agrachev, Marco Caponigro
  • 2008
1 Excerpt

Uniform convergence for elliptic problems on varying domains.Math. Nachr

  • Wolfgang Arendt, Daniel Daners
  • YANNICK PRIVAT AND MARIO SIGALOTTI
  • 2007
3 Excerpts

Characterization of the shape stability fo r n nlinear elliptic problems

  • Dorin Bucur
  • J. Differential Equations
  • 2006
3 Excerpts

Similar Papers

Loading similar papers…