Artículos de revistas
Self-adjointness of two-dimensional Dirac operators on corner domains
Fecha
2021Registro en:
Journal of Spectral Theory Volume 11 Issue 3 Page 1043-1079 Published 2021
10.4171/JST/365
Autor
Pizzichillo, Fabio
Van Den Bosch, Hanne
Institución
Resumen
We investigate the self-adjointness of the two-dimensional Dirac operator D, 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 description of the domain of the adjoint operator D* in terms of the domain of D and the set of harmonic functions that verify some mixed 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.