About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2001-2002), Talk no. 18, 10 p.

A non-homogeneous Hardy-like inequality has recently been found to be closely related to the knowledge of the lowest eigenvalue of a large class of Dirac operators in the gap of their continuous spectrum.

Dolbeault, Jean 1; Esteban, Maria J. 1; Séré, Eric 1

1 CEREMADE (UMR CNRS 7534) Université Paris-Dauphine F-75775 Paris Cedex 16
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Dolbeault, Jean; Esteban, Maria J.; Séré, Eric. About a non-homogeneous Hardy-inequality and its relation with the spectrum of Dirac operators. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2001-2002), Talk no. 18, 10 p. http://www.numdam.org/item/SEDP_2001-2002____A18_0/

[1] V.I. Burenkov, W.D. Evans. On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms. Proc. Roy. Soc. Edinburgh A, 128(5) (1998). p. 993-1005. | MR | Zbl

[2] S.N. Datta and G. Deviah. The minimax technique in relativistic Hartree-Fock calculations. Pramana, 30(5) (1988), p.387-405.

[3] J. Dolbeault, M.J. Esteban and E. Séré. Variational characterization for eigenvalues of Dirac operators. Cal. Var. 10 (2000), p. 321-347. | MR | Zbl

[4] J. Dolbeault, M.J. Esteban, E. Séré. On the eigenvalues of operators with gaps. Application to Dirac operators. J. Funct. Anal. 174 (2000), p. 208-226. | MR | Zbl

[5] J. Dolbeault, M.J. Esteban, E. Séré, M. Vanbreugel. Minimization methods for the one-particle Dirac equation. Phys. Rev. Letters 85(19) (2000), p. 4020-4023.

[6] J. Dolbeault, M.J. Esteban, E. Séré. A variational method for relativistic computations in atomic and molecular physics. To appear in Int. J. Quantum Chemistry.

[7] M.J. Esteban, E. Séré. Existence and multiplicity of solutions for linear and nonlinear Dirac problems. Partial Differential Equations and Their Applications. CRM Proceedings and Lecture Notes, volume 12. Eds. P.C. Greiner, V. Ivrii, L.A. Seco and C. Sulem. AMS, 1997. | MR | Zbl

[8] M. Griesemer, R.T. Lewis, H. Siedentop. A minimax principle in spectral gaps: Dirac operators with Coulomb potentials. Doc. Math. 4 (1999), P. 275-283 (electronic). | MR | Zbl

[9] M. Griesemer, H. Siedentop. A minimax principle for the eigenvalues in spectral gaps. J. London Math. Soc. (2) 60 no. 2 (1999), p. 490-500. | MR | Zbl

[10] M. Klaus and R. Wüst. Characterization and uniqueness of distinguished self-adjoint extensions of Dirac operators. Comm. Math. Phys. 64(2) (1978-79), p. 171-176. | MR | Zbl

[11] G. Nenciu. Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms. Comm. Math. Phys. 48 (1976), p. 235-247. | MR | Zbl

[12] U.W. Schmincke. Distinguished self-adjoint extensions of Dirac operators. Math. Z. 129 (1972), p. 335-349. | MR | Zbl

[13] J.D. Talman. Minimax principle for the Dirac equation. Phys. Rev. Lett. 57(9) (1986), p. 1091-1094. | MR

[14] B. Thaller. The Dirac Equation. Texts and Monographs in Physics. Springer-Verlag, Berlin, 1st edition, 1992. | MR | Zbl

[15] C. Tix. Strict Positivity of a relativistic Hamiltonian due to Brown and Ravenhall. Bull. London Math. Soc. 30(3) (1998), p. 283-290. | MR | Zbl

[16] R. Wüst. Dirac operators with strongly singular potentials. M ath. Z. 152 (1977), p. 259-271. | MR | Zbl