Comptes Rendus
Partial Differential Equations
Singular electromagnetic fields: inductive approach
Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, pp. 605-610.

In a non-convex polyhedral domain, we describe the local trace (i.e. defined on a face) of the normal derivative of an L2 function, with L2 Laplacian. We then provide generalized integration by parts formulae for the Laplace, divergence and curl operators. Finally, these results allow us to split electromagnetic fields into regular and singular parts, which can be characterized.

Dans le cas d'un domaine polyédrique non convexe, nous décrivons la trace locale (sur une face) de la dérivée normale d'une fonction L2, à Laplacien L2. On construit ensuite des formules d'intégration par parties généralisées pour les opérateurs Laplacien, divergence et rotationnel. Ceci permet enfin de décomposer les champs électromagnétiques en la somme d'un terme régulier et d'un terme singulier, que l'on caractérise.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2005.09.034
Franck Assous 1; Patrick Ciarlet 2; Emmanuelle Garcia 2

1 Department of Mathematics and Statistics, Bar-Ilan University, 52900 Ramat-Gan, Israël
2 CNRS-ENSTA-INRIA UMR 2706 POEMS, 32, boulevard Victor, 75739 Paris cedex 15, France
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Franck Assous; Patrick Ciarlet; Emmanuelle Garcia. Singular electromagnetic fields: inductive approach. Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, pp. 605-610. doi : 10.1016/j.crma.2005.09.034. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.034/

[1] F. Assous; P. Ciarlet C. R. Acad. Sci. Paris, Ser. I, 325 (1997), pp. 605-610

[2] F. Assous; P. Ciarlet; P.-A. Raviart; E. Sonnendrücker Math. Methods Appl. Sci., 22 (1999), pp. 485-499

[3] M.Sh. Birman; M.Z. Solomyak Siberian Math. J., 28 (1987), pp. 12-24

[4] A.S. Bonnet-Ben Dhia; C. Hazard; S. Lohrengel SIAM J. Appl. Math., 59 (1999), pp. 2028-2044

[5] A. Buffa; P. Ciarlet Math. Methods Appl. Sci., 24 (2001), pp. 9-48

[6] M. Costabel; M. Dauge Arch. Rational Mech. Anal., 151 (2000), pp. 221-276

[7] M. Costabel; M. Dauge; S. Nicaise Math. Models Numer. Anal., 33 (1999), pp. 627-649

[8] E. Garcia, PhD Thesis, Paris 6 University, France, 2002 (in French)

[9] C. Weber Math. Methods Appl. Sci., 2 (1980), pp. 12-25

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