MCS-MP Seminar: Hanne van den Bosch
Speaker: Hanne van den Bosch (Universidad de Chile)
Title: Dirac operators with delta-interactions supported on curves with corners.
Abstract: This talk concerns planar Dirac operators with special transmission boundary conditions along a curve, modeling the effect of a potential concentrating near this curve. In the case of smooth boundaries, it is by now well-understood that,
except for some special values of the coupling constant, this operator has a self-adjoint extension with domain in the first Sobolev space H^1. For corner domains one does not expect this to hold. Several authors constructed self-adjoint extensions in H^(1/2), depending on the type of potential and the exact assumptions on the curve with corners. In this seminar I will give an introduction to this kind of problem and present new results for the case of electrostatic potentials (proportional to the identity matrix).
This is based on joint work with Fabio Pizzichillo.