Surface integral formulation of the interior transmission problem

Anne Cossonnière 1 Houssem Haddar 1
1 DeFI - Shape reconstruction and identification
CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique, Inria Saclay - Ile de France, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR7641
Abstract : We consider a surface integral formulation of the so-called interior transmission problem that appears in the study of inverse scattering problems from dielectric inclusions. In the case where the magnetic permeability contrast is zero, the main originality of our approach consists in still using classical potentials for the Helmholtz equation but in weaker trace space solutions. One major outcome of this study is to establish Fredholm properties of the problem for relaxed assumptions on the material coefficients. For instance we allow the contrast to change sign inside the medium. We also show how one can retrieve discreteness results for transmission eigenvalues in some particular situations.
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Journal of Integral Equations and Applications, Rocky Mountain Mathematics Consortium, 2013, 25 (3), pp.341-376. 〈10.1216/JIE-2013-25-3-341〉
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Anne Cossonnière, Houssem Haddar. Surface integral formulation of the interior transmission problem. Journal of Integral Equations and Applications, Rocky Mountain Mathematics Consortium, 2013, 25 (3), pp.341-376. 〈10.1216/JIE-2013-25-3-341〉. 〈hal-00759128〉

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