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

@inproceedings{Drago2021TheCP, title={The Cauchy problem of the Lorentzian Dirac operator with APS boundary conditions}, author={Nicol{\`o} Drago and Nadine Gro{\ss}e and Simone Murro}, year={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…

## 5 Citations

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