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, GermanySimone Murro
Mathematisches Institut, Universität Freiburg, 79104 Freiburg, Germany
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