Volume 46, Number 6, November-December 2012
|Page(s)||1363 - 1387|
|Published online||11 April 2012|
T-coercivity for scalar interface problems between dielectrics and metamaterials
Laboratoire POEMS, UMR 7231 CNRS/ENSTA/INRIA, ENSTA ParisTech, 32, boulevard Victor, 75739 Paris Cedex 15, France
firstname.lastname@example.org; email@example.com; firstname.lastname@example.org
Received: 1 February 2011
Revised: 2 November 2011
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 dissipation 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 Fredholm (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.
Mathematics Subject Classification: 35Q60 / 35Q61 / 35J20
Key words: Metamaterials / interface problem / T-coercivity
© EDP Sciences, SMAI, 2012
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