@article{PieronekKleefeld2024,
  author    = {Pieronek, Lukas and Kleefeld, Andreas},
  title     = {On trajectories of complex-valued interior transmission eigenvalues},
  series = {Inverse problems and imaging : IPI},
  volume    = {18},
  journal   = {Inverse problems and imaging : IPI},
  number    = {2},
  publisher = {AIMS},
  address   = {Springfield, Mo},
  issn      = {1930-8337 (Print)},
  doi       = {10.3934/ipi.2023041},
  pages     = {480 -- 516},
  year      = {2024},
  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.},
  language  = {en}
}
@article{AyalaHarrisKleefeldetal.2023,
  author    = {Ayala, Rafael Ceja and Harris, Isaac and Kleefeld, Andreas and Pallikarakis, Nikolaos},
  title     = {Analysis of the transmission eigenvalue problem with two conductivity parameters},
  series = {Applicable Analysis},
  journal   = {Applicable Analysis},
  publisher = {Taylor \& Francis},
  issn      = {0003-6811},
  doi       = {10.1080/00036811.2023.2181167},
  pages     = {37 Seiten},
  year      = {2023},
  abstract  = {In this paper, we provide an analytical study of the transmission eigenvalue problem with two conductivity parameters. We will assume that the underlying physical model is given by the scattering of a plane wave for an isotropic scatterer. In previous studies, this eigenvalue problem was analyzed with one conductive boundary parameter whereas we will consider the case of two parameters. We prove the existence and discreteness of the transmission eigenvalues as well as study the dependence on the physical parameters. We are able to prove monotonicity of the first transmission eigenvalue with respect to the parameters and consider the limiting procedure as the second boundary parameter vanishes. Lastly, we provide extensive numerical experiments to validate the theoretical work.},
  language  = {en}
}