Un résultat de densité pour les équations de Maxwell régularisées dans un domaine lipschitzien

✍ Scribed by Martin Costabel; Monique Dauge

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 379 KB
• Volume: 327
• Category: Article
• ISSN: 0764-4442
• DOI: 10.1016/s0764-4442(99)80117-7

✦ Synopsis

Nous montrons la densite des fonctions rkgulibres dans I'espace des champs de vecteurs L' ?I divergence et rotationnel L", et dont la trace tangentielle (ou normale) est L' sur le bord. Notre dkmonstration est bake sur des thCor&mes de rCgularitC dans les domaines lipschitriens et constitue une simplification et une gCn&alisation du rksultat de [3]. G Acadkmie des Sciences/Elsevier, Paris A density result for the regularized Maxwell equations in a Lipschitz domain We show the density of smooth functions in the spuce of square integruble vector fields whose curl, divergence, and tangentinl (or normal) trace on the boundary ure square integrable. Our proof is based on the H"" regularity for the Dirichlet und Neumann problems and constitutes a simpli$cution and generalization of [3]. 0 Acad$mie des SciencesMsevier. Paris

A bridged Engiish Version

Let (1 be a bounded Lipschitz domain in R ', d = 2 or 3. Let W be the Hilbert space of vector fields that are square integrable on R together with their curl and divergence and whose tangential component is square integrable on dS2. This space with its natural norm, appears as energy space in certain variational formulations of electromagnetic boundary value problems, for example for the time-harmonic Maxwell equations "regularized" (see [ 1 I]) by the addition of a graddiv term. The boundary L* norm can correspond to weak formulations of impedance boundary conditions or a penalization of perfect conductor boundary conditions.

Note prCsentCe par kvariste SANCHEZ-PALENCIA.