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@ARTICLE{Harris:1048792,
      author       = {Harris, Isaac and Kleefeld, Andreas and Lee, Heejin},
      title        = {{E}xistence of transmission eigenvalues for biharmonic
                      scattering by a clamped planar region},
      journal      = {Inverse problems},
      volume       = {41},
      number       = {12},
      issn         = {0266-5611},
      address      = {Bristol [u.a.]},
      publisher    = {Inst.},
      reportid     = {FZJ-2025-04907},
      pages        = {125002},
      year         = {2025},
      abstract     = {In this paper, we study the so-called clamped transmission
                      eigenvalue problem. This is a new transmission eigenvalue
                      problem that is derived from the scattering of an
                      impenetrable clamped obstacle in a thin elastic plate. The
                      scattering problem is modeled by a biharmonic wave operator
                      given by the Kirchhoff-Love infinite plate problem in the
                      frequency domain. These scattering problems have not been
                      studied to the extent of other models. Unlike other
                      transmission eigenvalue problems, the problem studied here
                      is a system of homogeneous PDEs defined in all of
                      $\mathbb{R}^2$ . This provides unique analytical and
                      computational difficulties when studying the clamped
                      transmission eigenvalue problem. We are able to prove that
                      there exist infinitely many real clamped transmission
                      eigenvalues. This is done by studying the equivalent
                      variational formulation. We also investigate the
                      relationship of the clamped transmission eigenvalues to the
                      Dirichlet and Neumann eigenvalues of the negative Laplacian
                      for the bounded scattering obstacle.},
      cin          = {JSC},
      ddc          = {004},
      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},
      doi          = {10.1088/1361-6420/ae259b},
      url          = {https://juser.fz-juelich.de/record/1048792},
}