T-coercivity for scalar interface problems between dielectrics and metamaterials

Publication type:
Paper in peer-reviewed journals
Math. Mod. Num. Anal., vol. 46, pp. 1363–-1387
Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipa- tion is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of Rd, with d = 2, 3. Our aim is to characterize occurences where the problem is well-posed within the Fred- holm (or coercive + compact) framework. For that, we build some criteria, based on the geometry of the interface between the dielectric and the metamaterial. The proofs combine simple geometrical arguments with the approach of T-coercivity, introduced by the first and third authors and co-worker. Furthermore, the use of localization techniques allows us to derive well-posedness under conditions that involve the knowledge of the coefficients only near the interface. When the coefficients are piecewise constant, we establish the optimality of the criteria.
    author={Anne-Sophie Bonnet-BenDhia and Lucas Chesnel and Patrick 
           Ciarlet },
    title={T-coercivity for scalar interface problems between dielectrics 
           and metamaterials },
    doi={10.1051/m2an/2012006 },
    journal={Math. Mod. Num. Anal. },
    year={2012 },
    volume={46 },