APDE seminar@BCAM: Boundary value problems for 2-D Dirac operator on corner domains

We present recent results on self-adjoint extensions of Dirac operators on planar domains with corners under infinite-mass boundary conditions. Corners are shown to hinder the elliptic regularity valid for smooth boundaries.

We then extend the analysis to unbounded domains with infinitely many corners: the operator is self-adjoint when no concave corners are present, while in the concave case self-adjoint extensions arise. Among these, we single out a distinguished extension whose domain lies in a Sobolev space H^s, with s ≥ 1/2 depending on the corner opening.

Finally, we briefly present another related model involving delta-shell interactions and mention a forthcoming result in this direction.

The results presented come from different works in collaboration with Hanne Van Den Bosch and Miguel Camarasa.