Transmission eigenvalues for inhomogeneous media containing obstacles

Fioralba Cakoni, Anne Cossonnière Cerfacs, Houssem Haddar

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


We consider the interior transmission problem corresponding to the inverse scattering by an inhomogeneous (possibly anisotropic) media in which an impenetrable obstacle with Dirichlet boundary conditions is embed- ded. Our main focus is to understand the associated eigenvalue problem, more specifically to prove that the transmission eigenvalues form a discrete set and show that they exist. The presence of Dirichlet obstacle brings new difficul- ties to already complicated situation dealing with a non-selfadjoint eigenvalue problem. In this paper, we employ a variety of variational techniques under various assumptions on the index of refraction as well as the size of the Dirichlet obstacle.

Original languageEnglish (US)
Pages (from-to)373-398
Number of pages26
JournalInverse Problems and Imaging
Issue number3
StatePublished - Aug 2012
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Modeling and Simulation
  • Discrete Mathematics and Combinatorics
  • Control and Optimization


  • Inhomoge-neous medium
  • Interior transmission problem
  • Inverse scattering problem
  • Transmission eigenvalues


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