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

2021/04/01 by Nicolò Drago, Drago, Nicolò, Nadine Große +3
Mathematics · #53C27 #58J45 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Primary 35L50 #Secondary 53C50 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2104.00585

openalex publication_date 2021/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Generalized cylinders in semi-Riemannian and spin geometry
• On Smooth Cauchy Hypersurfaces and Geroch’s Splitting Theorem
• The quantum theory of the electron

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• The Cauchy problem for Lorentzian Dirac operators under non-local boundary conditions
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