Description
This talk aims to present results on the self-adjoint extensions of Dirac operators on plane domains with corners in dimension two. We consider the case of infinite-mass boundary conditions and we obtain explicitly the self-adjoint extensions of the operator. It turns out that the presence of corners typically spoils the elliptic regularity known to hold for smooth boundaries.
Then we discuss the self-adjointness and some spectral properties of these operators in presence of a Coulomb-type potential with the singularity placed on the vertex.
This is a collaboration work with Hanne Van Den Bosch, Biagio Cassano and Matteo Gallone.
