Self-adjoint Dirac operators with boundary conditions on domains

Mercredi 29 novembre 2017 16:00-17:00 - Markus Holzmann - TU Graz

Résumé : Let $\Omega \subset\mathbbR^3$ be a domain with compact $C^2$-smooth boundary.
In this talk we discuss Dirac operators on $\Omega$ acting on functions which satisfy
suitable boundary conditions which yield self-adjoint operators in $L^2(\Omega ; \mathbbC^4)$.
Such operators are the relativistic counterparts of Laplacians on $\Omega$ with Robin-type boundary conditions. Using a boundary triple approach the self-adjointness of the operators can be shown.
It turns out that there exist critical boundary values for which functions in the domains of the corresponding operators have less Sobolev-regularity.
Furthermore, several basic spectral properties of the operators are obtained,
which can be analyzed and formulated in terms of well-studied integral operators for the Dirac equation.
This talk is based on a joint work with J. Behrndt and A. Mas.

Lieu : salle 229, bâtiment 440

Self-adjoint Dirac operators with boundary conditions on domains  Version PDF