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Ground state energy of the magnetic Laplacian on corner domains

hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
dc.contributor.authorBONNAILLIE-NOËL, Virginie
hal.structure.identifierInstitut de Recherche Mathématique de Rennes [IRMAR]
dc.contributor.authorDAUGE, Monique
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPOPOFF, Nicolas
dc.date.accessioned2024-04-04T03:16:26Z
dc.date.available2024-04-04T03:16:26Z
dc.date.issued2016
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194214
dc.description.abstractEnThe 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.
dc.description.sponsorshipCentre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
dc.language.isoen
dc.publisher.locationParis
dc.title.enGround state energy of the magnetic Laplacian on corner domains
dc.typeOuvrage
dc.subject.halMathématiques [math]/Théorie spectrale [math.SP]
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halPhysique [physics]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Physique mathématique [math-ph]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
dc.identifier.arxiv1403.7043
bordeaux.page138
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-00966863
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00966863v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2016&rft.spage=138&rft.epage=138&rft.au=BONNAILLIE-NO%C3%8BL,%20Virginie&DAUGE,%20Monique&POPOFF,%20Nicolas&rft.genre=unknown


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