Compact imbeddings in electromagnetism with interfaces between classical materials and meta-materials

Lucas Chesnel 1 Patrick Ciarlet 1, *
* Auteur correspondant
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, ENSTA ParisTech UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : In a meta-material, the electric permittivity and/or the magnetic permeability can be negative in given frequency ranges. We investigate the solution of the time-harmonic Maxwell equations in a composite material, made up of classical materials, and meta-materials with negative electric permittivity, in a two-dimensional bounded domain Ω. We study the imbedding of the space of electric fields into L²(Ω)². In particular, we extend the famous result of Weber, proving that it is compact. This result is obtained by studying the regularity of the fields. We first isolate their most singular part, using a decomposition à la Birman-Solomyak. With the help of the Mellin transform, we prove that this singular part belongs to Hˢ(Ω)², for some s > 0. Finally, we show that the compact imbedding result holds as soon as no ratio of permittivities between two adjacent materials is equal to −1.
Type de document :
Pré-publication, Document de travail
21 pages. 2011
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00602904
Contributeur : Patrick Ciarlet <>
Soumis le : jeudi 23 juin 2011 - 16:41:02
Dernière modification le : vendredi 10 février 2017 - 01:12:40
Document(s) archivé(s) le : samedi 24 septembre 2011 - 02:26:18

Fichier

ChCi11-accepted.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

  • HAL Id : hal-00602904, version 1

Collections

Citation

Lucas Chesnel, Patrick Ciarlet. Compact imbeddings in electromagnetism with interfaces between classical materials and meta-materials. 21 pages. 2011. <hal-00602904>

Partager

Métriques

Consultations de
la notice

499

Téléchargements du document

150