A POINCARÉ-STEKLOV MAP FOR THE MIT BAG MODEL
BENHELLAL, Badreddine
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Departamento de Matemáticas [Bilbao]
Basque Center for Applied Mathematics [BCAM]
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Departamento de Matemáticas [Bilbao]
Basque Center for Applied Mathematics [BCAM]
ZREIK, Mahdi
Institut de Mathématiques de Bordeaux [IMB]
Universidad del País Vasco [Espainia] / Euskal Herriko Unibertsitatea [España] = University of the Basque Country [Spain] = Université du pays basque [Espagne] [UPV / EHU]
Departamento de Matemáticas [Bilbao]
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Universidad del País Vasco [Espainia] / Euskal Herriko Unibertsitatea [España] = University of the Basque Country [Spain] = Université du pays basque [Espagne] [UPV / EHU]
Departamento de Matemáticas [Bilbao]
Université de Bordeaux [UB]
BENHELLAL, Badreddine
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Departamento de Matemáticas [Bilbao]
Basque Center for Applied Mathematics [BCAM]
Université de Bordeaux [UB]
Institut de Mathématiques de Bordeaux [IMB]
Departamento de Matemáticas [Bilbao]
Basque Center for Applied Mathematics [BCAM]
ZREIK, Mahdi
Institut de Mathématiques de Bordeaux [IMB]
Universidad del País Vasco [Espainia] / Euskal Herriko Unibertsitatea [España] = University of the Basque Country [Spain] = Université du pays basque [Espagne] [UPV / EHU]
Departamento de Matemáticas [Bilbao]
Université de Bordeaux [UB]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Universidad del País Vasco [Espainia] / Euskal Herriko Unibertsitatea [España] = University of the Basque Country [Spain] = Université du pays basque [Espagne] [UPV / EHU]
Departamento de Matemáticas [Bilbao]
Université de Bordeaux [UB]
Language
en
Document de travail - Pré-publication
English Abstract
The 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 ...Read more >
The 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.Read less <
Origin
Hal imported