Self-Adjointness of two dimensional Dirac operators on corner domains

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.