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A NEW COMPACTNESS RESULT FOR ELECTROMAGNETIC WAVES: APPLICATION TO THE TRANSMISSION PROBLEM BETWEEN DIELECTRICS AND METAMATERIALS

    https://doi.org/10.1142/S0218202508003145Cited by:14 (Source: Crossref)

    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 L2. 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.

    AMSC: 22E46, 53C35, 57S20

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