Boundary integral equations for the transmission eigenvalue problem for Maxwell's equations

Fioralba Cakoni, Houssem Haddar, Shixu Meng, Giovanni Monegato

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10 Scopus citations

Abstract

In this paper, we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission eigenvalue problem as an equivalent homogeneous system of the boundary integral equation and, assuming that the contrast is constant near the boundary of the support of the inhomogeneity, we prove that the operator associated with this system is Fredholm of index zero and depends analytically on the wave number. Then we show the existence of wave numbers that are not transmission eigenvalues which by an application of the analytic Fredholm theory implies that the set of transmission eigenvalues is discrete with positive infinity as the only accumulation point.

Original languageEnglish (US)
Pages (from-to)375-406
Number of pages32
JournalJournal of Integral Equations and Applications
Volume27
Issue number3
DOIs
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Numerical Analysis

Keywords

  • Boundary integral equations
  • Inverse scattering
  • Maxwell's equations
  • the transmission eigenvalue problem

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