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Variational characterization for eigenvalues of Dirac operators

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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.

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Authors and Affiliations

  1. Ceremade (UMR CNRS 7534) CNRS et Université Paris-Dauphine, Place Maréchal Lattre de Tassigny, F-75775 Paris Cedex 16, France, , , , , , FR

    Jean Dolbeault, Maria J. Esteban & Eric Séré

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  1. Jean Dolbeault
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  2. Maria J. Esteban
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  3. Eric Séré
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Received June 5, 1998 / Accepted June 11, 1999

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Dolbeault, J., Esteban, M. & Séré, E. Variational characterization for eigenvalues of Dirac operators. Calc Var 10, 321–347 (2000). https://doi.org/10.1007/s005260010321

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  • DOI: https://doi.org/10.1007/s005260010321

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