Geodesic
The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary
Documenta mathematica, Tome 25 (2020), pp. 737-765
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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.
DOI : 10.4171/dm/761
Classification : 35L50, 35Q75, 53C50, 58J32, 58J45
Mots-clés : Cauchy problem, Dirac operator, initial-boundary value problem, MIT-boundary conditions 
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     title = {The {Well-Posedness} of the {Cauchy} {Problem} for the {Dirac} {Operator} on {Globally} {Hyperbolic} {Manifolds} with {Timelike} {Boundary}},
     journal = {Documenta mathematica},
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Nadine Grosse; Simone Murro. The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary. Documenta mathematica, Tome 25 (2020), pp. 737-765. doi: 10.4171/dm/761

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