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Pré-Publication, Document De Travail Année : 2019

Self-Adjointness of two dimensional Dirac operators on corner domains

Résumé

We study the self-adjointenss of the two-dimensional Dirac operator with Quantum-dot and Lorentz-scalar $\delta$-shell boundary conditions, on piecewise $C^2$ 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 $H^{1/2}$, 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.

Dates et versions

hal-02018711 , version 1 (14-02-2019)

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Fabio Pizzichillo, Hanne van Den Bosch. Self-Adjointness of two dimensional Dirac operators on corner domains. 2019. ⟨hal-02018711⟩
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