BONNAILLIE-NOËL, Virginie; DAUGE, Monique; POPOFF, Nicolas

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BONNAILLIE-NOËL, Virginie
Département de Mathématiques et Applications - ENS Paris [DMA]

DAUGE, Monique
Institut de Recherche Mathématique de Rennes [IRMAR]

POPOFF, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

Langue

Ouvrage

Ce document a été publié dans

2016p. 138

Résumé en anglais

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in smooth three-dimensional domains is characterized by model problems inside the domain or on its boundary. In two-dimensional polygonal domains, a new set of model problems on sectors has to be taken into account. In this paper, we consider the class of general corner domains. In dimension 3, they include as particular cases polyhedra and axisymmetric cones. We attach model problems not only to each point of the closure of the domain, but also to a hierarchy of ''tangent substructures'' associated with singular chains. We investigate properties of these model problems, namely continuity, semi-continuity, existence of generalized eigenfunctions satisfying exponential decay. We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with the help of an IMS partition based on adequate two-scale coverings of the corner 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 part of our analysis extends to any dimension.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194214

Project ANR

Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251