The Electromagnetic Interior Transmission Problem for Regions with Cavities

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 the electromagnetic interior transmission problem in the case when the medium has cavities, i.e. regions in which the index of refraction is the same as in the host medium. We address the configuration where the electromagnetic permeability is constant while the electric permittivity is variable and may be anisotropic. In this case, using appropriate reformulation of the problem into a fourth order pde, we establish the Fredholm property for this problem and show that transmission eigenvalues exist and form a discrete set. Monotonicity properties of the first eigenvalue in terms of the permittivity and the size of the cavity are established.
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SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43 (4), pp.1698-1715. 〈10.1137/100813890〉
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Anne Cossonnière, Houssem Haddar. The Electromagnetic Interior Transmission Problem for Regions with Cavities. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2011, 43 (4), pp.1698-1715. 〈10.1137/100813890〉. 〈hal-00743733〉

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