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A POINCARÉ-STEKLOV MAP FOR THE MIT BAG MODEL

hal.structure.identifierUniversité de Bordeaux [UB]
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierDepartamento de Matemáticas [Bilbao]
hal.structure.identifierBasque Center for Applied Mathematics [BCAM]
dc.contributor.authorBENHELLAL, Badreddine
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBRUNEAU, Vincent
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierUniversidad del País Vasco [Espainia] / Euskal Herriko Unibertsitatea [España] = University of the Basque Country [Spain] = Université du pays basque [Espagne] [UPV / EHU]
hal.structure.identifierDepartamento de Matemáticas [Bilbao]
hal.structure.identifierUniversité de Bordeaux [UB]
dc.contributor.authorZREIK, Mahdi
dc.date.accessioned2024-04-04T02:40:28Z
dc.date.available2024-04-04T02:40:28Z
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191067
dc.description.abstractEnThe purpose of this paper is to introduce and study Poincaré-Steklov (PS) operators associated to the Dirac operator Dm with the so-called MIT bag boundary condition. In a domain Ω ⊂ R 3 , for a complex number z and for Uz a solution of (Dm − z)Uz = 0, the associated PS operator maps the value of Γ − Uz, the MIT bag boundary value of Uz, to Γ + Uz, where Γ ± are projections along the boundary ∂Ω and (Γ − + Γ +) = t ∂Ω is the trace operator on ∂Ω. In the first part of this paper, we show that the PS operator is a zero-order pseudodifferential operator and give its principal symbol. In the second part, we study the PS operator when the mass m is large, and we prove that it fits into the framework of 1/m-pseudodifferential operators, and we derive some important properties, especially its semiclassical principal symbol. Subsequently, we apply these results to establish a Krein-type resolvent formula for the Dirac operator H M = Dm + M β1 R 3 \Ω for large masses M > 0, in terms of the resolvent of the MIT bag operator on Ω. With its help, the large coupling convergence with a convergence rate of O(M −1) is shown.
dc.language.isoen
dc.title.enA POINCARÉ-STEKLOV MAP FOR THE MIT BAG MODEL
dc.typeDocument de travail - Pré-publication
dc.subject.halMathématiques [math]
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-03706471
hal.version1
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03706471v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BENHELLAL,%20Badreddine&BRUNEAU,%20Vincent&ZREIK,%20Mahdi&rft.genre=preprint


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