On the existence of transmission eigenvalues in an inhomogeneous medium

Fioralba Cakoni, Houssem Haddar

Research output: Contribution to journalArticle

65 Citations (Scopus)

Abstract

We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both the scalar problem and Maxwell's equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Paivarinta and Sylvester [Transmission eigenvalues, SIAM J. Math. Anal. 40, (2008) pp. 783-753] to prove the existence of transmission eigenvalues for a larger class of interior transmission problems. Our analysis includes both the case of a medium with positive contrast and of a medium with negative contrast provided that the contrasts are large enough.

Original languageEnglish (US)
Pages (from-to)475-493
Number of pages19
JournalApplicable Analysis
Volume88
Issue number4
DOIs
StatePublished - Apr 1 2009

Fingerprint

Inhomogeneous Media
Eigenvalue
Anisotropic Media
Transmission Problem
Inverse Scattering Problem
Maxwell's equations
Anisotropic media
Eigenvalue Problem
Maxwell equations
Interior
Scalar
Scattering

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

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

Cite this

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On the existence of transmission eigenvalues in an inhomogeneous medium. / Cakoni, Fioralba; Haddar, Houssem.

In: Applicable Analysis, Vol. 88, No. 4, 01.04.2009, p. 475-493.

Research output: Contribution to journalArticle

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