Variational characterization for eigenvalues of Dirac operators
- Cite this article as:
- Dolbeault, J., Esteban, M. & Séré, E. Calc Var (2000) 10: 321. doi:10.1007/s005260010321
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.