|
Résumé : |
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. |
