• DOI:10.1137/100793542
• Corpus ID: 18381807

The Interior Transmission Eigenvalue Problem

@article{Cakoni2010TheIT,
  title={The Interior Transmission Eigenvalue Problem},
  author={Fioralba Cakoni and David Colton and Drossos Gintides},
  journal={SIAM J. Math. Anal.},
  year={2010},
  volume={42},
  pages={2912-2921}
}

• F. Cakoni, D. Colton, D. Gintides
• Published 30 November 2010
• Mathematics
• SIAM J. Math. Anal.

We consider the inverse problem of determining the spherically symmetric index of refraction $n(r)$ from a knowledge of the corresponding transmission eigenvalues (which can be determined from field pattern of the scattered wave). We also show that for constant index of refraction $n(r)=n$, the smallest transmission eigenvalue suffices to determine n, complex eigenvalues exist for n sufficiently small and, for homogeneous media of general shape, determine a region in the complex plane where complex eigenvalues must lie.