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

Nicolò Drago, Nadine Große, Simone Murro
April 01, 2021
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.

Cauchy problem, classical Dirac operator, APS boundary condition, globally hyperbolic manifold with timelike boundary.