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

  • Nadine Grosse

    Mathematisches Institut, Universität Freiburg, 79104 Freiburg, Germany
  • Simone Murro

    Mathematisches Institut, Universität Freiburg, 79104 Freiburg, Germany
The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary cover
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Abstract

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.

Cite this article

Nadine Grosse, Simone Murro, The Well-Posedness of the Cauchy Problem for the Dirac Operator on Globally Hyperbolic Manifolds with Timelike Boundary. Doc. Math. 25 (2020), pp. 737–765

DOI 10.4171/DM/761