Calculus of Variations and Partial Differential Equations

, Volume 10, Issue 4, pp 321–347

Variational characterization for eigenvalues of Dirac operators

Authors

  • Jean Dolbeault
    • Ceremade (UMR CNRS 7534) CNRS et Université Paris-Dauphine, Place Maréchal Lattre de Tassigny, F-75775 Paris Cedex 16, France
  • Maria J. Esteban
    • Ceremade (UMR CNRS 7534) CNRS et Université Paris-Dauphine, Place Maréchal Lattre de Tassigny, F-75775 Paris Cedex 16, France
  • Eric Séré
    • Ceremade (UMR CNRS 7534) CNRS et Université Paris-Dauphine, Place Maréchal Lattre de Tassigny, F-75775 Paris Cedex 16, France
Original article

DOI: 10.1007/s005260010321

Cite this article as:
Dolbeault, J., Esteban, M. & Séré, E. Calc Var (2000) 10: 321. doi:10.1007/s005260010321

Abstract.

In this paper we give two different variational characterizations for the eigenvalues of H+V where H denotes the free Dirac operator and V is a scalar potential. The first one is a min-max involving a Rayleigh quotient. The second one consists in minimizing an appropriate nonlinear functional. Both methods can be applied to potentials which have singularities as strong as the Coulomb potential.

Mathematics Subject Classification (1991): 49R05, 49R10, 49R20, 49S05, 47A75, 81Q10, 35P05, 35Q75, 35A15

Copyright information

© Springer-Verlag Berlin Heidelberg 2000