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

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

Franck Assous, Patrick Ciarlet, Simon Labrunie

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3 Scopus citations

Abstract

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.

Translated title of the contribution	Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain
Original language	English
Pages (from-to)	767-772
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	328
Issue number	9
DOIs	https://doi.org/10.1016/S0764-4442(99)80269-9
State	Published - May 1999
Externally published	Yes

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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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