The Cauchy problem of the Lorentzian Dirac operator with APS boundary conditions

Abstract

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.

We identified an error in Section 4.2.3: the proof that the solution of the regularized problem still satisfies APS is missing. Addressing this would require substantial revisions, so we have decided to withdraw the paper

Cited by in corpus (1)

• On the Cauchy problem for Friedrichs systems on globally hyperbolic manifolds with timelike boundary