Grosse, Nadine; Murro, Simone

The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary

Doc. Math. 25, 737-765 (2020)
DOI: 10.25537/dm.2020v25.737-765
Communicated by Christian Bär


We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem locally into a symmetric positive hyperbolic system, proving existence and uniqueness of weak solutions and then using local methods developed by Lax, Phillips and Rauch, Massey to show smoothness of the solutions. Our proof actually works for a slightly more general class of local boundary conditions.

Mathematics Subject Classification

58J32, 58J45, 53C50, 35L50, 35Q75


Dirac operator, initial-boundary value problem, Cauchy problem, MIT-boundary conditions


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Grosse, Nadine
Mathematisches Institut, Universität Freiburg, 79104 Freiburg, Germany
Murro, Simone
Mathematisches Institut, Universität Freiburg, 79104 Freiburg, Germany