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@ARTICLE{Pieronek:1025792,
      author       = {Pieronek, Lukas and Kleefeld, Andreas},
      title        = {{O}n trajectories of complex-valued interior transmission
                      eigenvalues},
      journal      = {Inverse problems and imaging},
      volume       = {18},
      number       = {2},
      issn         = {1930-8337},
      address      = {Springfield, Mo.},
      publisher    = {AIMS},
      reportid     = {FZJ-2024-03155},
      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.},
      cin          = {JSC},
      ddc          = {510},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {5112 - Cross-Domain Algorithms, Tools, Methods Labs (ATMLs)
                      and Research Groups (POF4-511)},
      pid          = {G:(DE-HGF)POF4-5112},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:001072416100001},
      doi          = {10.3934/ipi.2023041},
      url          = {https://juser.fz-juelich.de/record/1025792},
}