Higher dimensional transmission problems for Dirac operators on Lipschitz domains

Autor: Ariel Hernández Herrera
Transmission boundary value problems for the time-harmonic Maxwell system, the Helmholtz operator, and the perturbed Dirac operator are formulated, using Clifford algebras, on bounded Lipschitz domains of $ \R^{m} $ with ${m \geq 3}$. It is shown how the Dirac problem decouples into several Maxwell and Helmholtz problems. Necessary and sufficient conditions are provided for well-posedness in each case, and for the Dirac problem to be equivalent to one or several independent Maxwell problems.