On trajectories of complex-valued interior transmission eigenvalues

Inverse Problems and Imaging, vol. 0, pp. 0

Abstract

This paper investigates the interior transmission problem for homogeneous media via eigenvalue trajectories parameterized by the magnitude of the refractive index. In the case that the scatterer is the unit disk, we prove that there is a one-to-one correspondence between complex-valued interior transmission eigenvalue trajectories and Dirichlet eigenvalues of the Laplacian which turn out to be exactly the trajectorial limit points as the refractive index tends to infinity. For general simply-connected scatterers in two or three dimensions, a corresponding relation is still open, but further theoretical results and numerical studies indicate a similar connection.

Authors 2

1. Lukas Pieronek corresponding

   Karlsruhe Institute of Technology

   Affiliation as printed

   Karlsruhe Institute of Technology , Institute for Applied and Numerical Mathematics Englerstr. 2 , 76131 Karlsruhe , Germany

   Karlsruhe Institute of Technology, Institute for Applied and Numerical Mathematics Englerstr. 2, 76131 Karlsruhe, Germany

2. Andreas Kleefeld Aachen

   FH Aachen · Forschungszentrum Jülich · Jülich Supercomputing Centre

   Affiliation as printed

   Forschungszentrum Jülich GmbH , Jülich Supercomputing Centre Wilhelm-Johnen-Str. , 52425 Jülich , Germany

   University of Applied Sciences Aachen Faculty of Medical Engineering and Technomathematics Heinrich-Mußmann-Str. 1 , 52428 Jülich , Germany

   Faculty of Medical Engineering and Technomathematics Heinrich-Mußmann-Str. 1, 52428 Jülich, Germany

   Forschungszentrum Jülich GmbH, Jülich Supercomputing Centre Wilhelm-Johnen-Str., 52425 Jülich, Germany

   University of Applied Sciences Aachen