Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain

Franck Assous; Patrick Ciarlet; Simon Labrunie

doi:10.1016/S0764-4442(99)80269-9

Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain

Titre traduit de la contribution: Caractérisation des singularités et résolution des équations de Maxwell stationnaires en géométrie axisymétrique

Franck Assous
, Patrick Ciarlet
, Simon Labrunie

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

We study the steady-state Maxwell equations in a non-smooth, non-convex, axially symmetric domain Ω. The solutions are written as the orthogonal sum of a regular part within H¹ (Ω)³, and a singular part. We show that, like in the two-dimensional case, the singular part is related to the (axisymmetric) singular eigenfuctions of the Laplacian, and hence is of finite dimension.

Titre traduit de la contribution	Caractérisation des singularités et résolution des équations de Maxwell stationnaires en géométrie axisymétrique
langue originale	Anglais
Pages (de - à)	767-772
Nombre de pages	6
journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	328
Numéro de publication	9
Les DOIs	https://doi.org/10.1016/S0764-4442(99)80269-9
état	Publié - 1 janv. 1999

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10.1016/S0764-4442(99)80269-9

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Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain. / Assous, Franck; Ciarlet, Patrick; Labrunie, Simon.
Dans: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol 328, Numéro 9, 01.01.1999, p. 767-772.

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

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N2 - We study the steady-state Maxwell equations in a non-smooth, non-convex, axially symmetric domain Ω. The solutions are written as the orthogonal sum of a regular part within H1 (Ω)3, and a singular part. We show that, like in the two-dimensional case, the singular part is related to the (axisymmetric) singular eigenfuctions of the Laplacian, and hence is of finite dimension.

AB - We study the steady-state Maxwell equations in a non-smooth, non-convex, axially symmetric domain Ω. The solutions are written as the orthogonal sum of a regular part within H1 (Ω)3, and a singular part. We show that, like in the two-dimensional case, the singular part is related to the (axisymmetric) singular eigenfuctions of the Laplacian, and hence is of finite dimension.

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Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain

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