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Self-Adjointness of two dimensional Dirac operators on corner domains

Pizzichillo, Fabio; Bosch, Hanne Van Den (2019), Self-Adjointness of two dimensional Dirac operators on corner domains. https://basepub.dauphine.fr/handle/123456789/18664

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02018711
Date
2019
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
21
Metadata
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Author(s)
Pizzichillo, Fabio
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Bosch, Hanne Van Den
Abstract (EN)
We study the self-adjointenss of the two-dimensional Dirac operator with Quantum-dot and Lorentz-scalar δ-shell boundary conditions, on piecewise C2 domains with finitely many corners. For both models, we prove the existence of a unique self-adjoint realization whose domain is included in the Sobolev space H1/2, the formal form domain of the free Dirac operator. The main part of our paper consists of a detailed study of the problem on an infinite sector, where explicit computations can be made: we find the self-adjoint extensions for this case. The result is then translated to general domains by a coordinate transformation.
Subjects / Keywords
Dirac operators; self-adjointenss