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

Franck Assous
, Patrick Ciarlet
, Simon Labrunie

Research output: Contribution to journal › Article › peer-review

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	Caractérisation des singularités et résolution des équations de Maxwell stationnaires en géométrie axisymétrique
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
Publication status	Published - 1 Jan 1999

Access to Document

10.1016/S0764-4442(99)80269-9

Cite this

@article{273201f9118642d1b23ec9f16e62ac24,

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

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.",

author = "Franck Assous and Patrick Ciarlet and Simon Labrunie",

year = "1999",

month = jan,

day = "1",

doi = "10.1016/S0764-4442(99)80269-9",

language = "English",

volume = "328",

pages = "767--772",

journal = "Comptes Rendus de l'Academie des Sciences - Series I: Mathematics",

issn = "0764-4442",

number = "9",

}

TY - JOUR

T1 - Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain

AU - Assous, Franck

AU - Ciarlet, Patrick

AU - Labrunie, Simon

PY - 1999/1/1

Y1 - 1999/1/1

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.

UR - https://www.scopus.com/pages/publications/0033131489

U2 - 10.1016/S0764-4442(99)80269-9

DO - 10.1016/S0764-4442(99)80269-9

M3 - Article

AN - SCOPUS:0033131489

SN - 0764-4442

VL - 328

SP - 767

EP - 772

JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

IS - 9

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this