A new compactness result for electromagnetic waves. Application to the transmission problem between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia 1 Patrick Ciarlet 1 Carlo Maria Zwölf 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 : We consider the time-harmonic Maxwell equations, involving wave transmission between media with opposite sign dielectric and/or magnetic coefficients. We prove that, in the case of sign-shifting dielectric coefficients, the space of electric fields is compactly embedded in L 2. We build a three-field variational formulation equivalent to Maxwell system for sign-shifting magnetic coefficients and show that, under some suitable conditions, the formulation fits into the coercive plus compact framework. © 2008 World Scientific Publishing Company.
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Submitted on : Thursday, October 17, 2013 - 2:04:15 PM
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Anne-Sophie Bonnet-Ben Dhia, Patrick Ciarlet, Carlo Maria Zwölf. A new compactness result for electromagnetic waves. Application to the transmission problem between dielectrics and metamaterials. Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 2008, 18 (9), pp.1605-1631. ⟨10.1142/s0218202508003145⟩. ⟨hal-00873080⟩

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