98-177 J. Dolbeault, M.J. Esteban, E. Sere

Variational characterization for eigenvalues of Dirac operators (1036K, Postscript) Mar 10, 98

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Abstract. In this paper we give two different variational characterizations for the eigenvalues of 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.

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