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Self-Adjointness of two dimensional Dirac operators on corner domains

Pizzichillo, Fabio; Bosch, Hanne Van Den (2021), Self-Adjointness of two dimensional Dirac operators on corner domains, Journal of Spectral Theory, 11, 3, p. 1043–1079. 10.4171/JST/365

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Journal of Spectral Theory
Volume
11
Number
3
Publisher
European Mathematical Society
Published in
Paris
Pages
1043–1079
Publication identifier
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