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Rapport Année : 2013

Ground Energy of the Magnetic Laplacian in Polyhedral Bodies

Résumé

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the model problems (continuity, semi-continuity, existence of generalized eigenfunctions). We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with the help of a classical IMS partition based on adequate coverings of the polyhedral domain, whereas upper bounds are established by a novel construction of quasimodes, qualified as sitting or sliding according to spectral properties of local model problems.

A more complete version of this work, including the treatment of non-polyhedral cones, is available at http://hal.archives-ouvertes.fr/hal-00966863
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Dates et versions

hal-00864272 , version 1 (20-09-2013)
hal-00864272 , version 2 (04-11-2013)
hal-00864272 , version 3 (04-12-2013)

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Virginie Bonnaillie-Noël, Monique Dauge, Nicolas Popoff. Ground Energy of the Magnetic Laplacian in Polyhedral Bodies. 2013. ⟨hal-00864272v3⟩
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