TY  - JOUR
A1  - Pieronek, Lukas
A1  - Kleefeld, Andreas
T1  - On trajectories of complex-valued interior transmission eigenvalues
JF  - Inverse problems and imaging : IPI
N2  - 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.
KW  - Interior transmission problem
KW  - Eigenvalue trajectories
KW  - Complex-valued eigenvalues
Y1  - 2024
U6  - http://dx.doi.org/10.3934/ipi.2023041
SN  - 1930-8337 (Print)
SN  - 1930-8345 (Online)
VL  - 18
IS  - 2
SP  - 480
EP  - 516
PB  - AIMS
CY  - Springfield, Mo
ER  -