Self-adjointness of two-dimensional Dirac operators on corner domains
Fabio Pizzichillo
CNRS & Université Paris Dauphine, FranceHanne Van Den Bosch
Universidad de Chile & UMI–CNRS, Santiago, Chile
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Abstract
We investigate the self-adjointness of the two-dimensional Dirac operator , with - and - - boundary conditions, on piecewise 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 , the formal form domain of the free Dirac operator. The main part of our paper consists of a description of the domain of the adjoint operator in terms of the domain of and the set of harmonic functions that verify some boundary conditions. Then, we give 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.
Cite this article
Fabio Pizzichillo, Hanne Van Den Bosch, Self-adjointness of two-dimensional Dirac operators on corner domains. J. Spectr. Theory 11 (2021), no. 3, pp. 1043–1079
DOI 10.4171/JST/365