On the self-adjointness of two-dimensional relativistic shell interactions

We discuss the self-adjointness of the two-dimensional Dirac operator with a transmission condition along a closed Lipschitz curve. The new self-adjointness condition includes and extends all previous results for this class of problems. The study is particularly precise for the case of curvilinear polygons, as the angles can be taken into account in an explicit way. In particular, if the curve is a curvilinear polygon with obtuse angles, then there is a unique self-adjoint realization with domain contained in H1/2 for the full range of non-critical coefficients in the transmission condition.