The Interior Transmission Problem for Regions with Cavities

@article{Cakoni2010TheIT,
  title={The Interior Transmission Problem for Regions with Cavities},
  author={Fioralba Cakoni and David Colton and Houssem Haddar},
  journal={SIAM J. Math. Anal.},
  year={2010},
  volume={42},
  pages={145-162}
}
We consider the interior transmission problem in the case when the inhomogeneous medium has cavities, i.e., regions in which the index of refraction is the same as the host medium. In this case we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. We also derive Faber–Krahn-type inequalities for the transmission eigenvalues. 

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