Interior transmission eigenvalue problem for Maxwell's equations: The T-coercivity as an alternative approach

Lucas Chesnel 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In this paper, we examine the interior transmission problem for Maxwells equations in the case where both and , the physical parameters of the scattering medium, differ from 0 and 0 modelling the background medium. Using the T-coercivity method, we propose an alternative approach to the classical techniques to prove that this problem is of Fredholm type and that the so-called transmission eigenvalues form at most a discrete set. The T-coercivity approach allows us to deal with cases where 0 and 0 can change sign. We also provide results of localization and FaberKrahn-type inequalities for the transmission eigenvalues. © 2012 IOP Publishing Ltd.
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Lucas Chesnel. Interior transmission eigenvalue problem for Maxwell's equations: The T-coercivity as an alternative approach. Inverse Problems, IOP Publishing, 2012, 28 (6), ⟨10.1088/0266-5611/28/6/065005⟩. ⟨hal-00849561⟩

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