  We consider the classical Dirac operator on globally hyperbolic manifolds
with timelike boundary and show well-posedness of the Cauchy initial-boundary
value problem coupled to APS-boundary conditions. This is achieved by deriving
suitable energy estimates, which play a fundamental role in establishing
uniqueness and existence of weak solutions. Finally, by introducing suitable
mollifier operators, we study the differentiability of the solutions. For
obtaining smoothness we need additional technical conditions.
