The interior transmission eigenvalue problem

Fioralba Cakoni, David Colton, Drossos Gintides

Research output: Contribution to journalArticle

52 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2912-2921
Number of pages10
JournalSIAM Journal on Mathematical Analysis
Volume42
Issue number6
DOIs
StatePublished - Dec 1 2010
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Inhomogeneous medium
  • Interior transmission problem
  • Inverse scattering
  • Transmission eigenvalues

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