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Solution of axisymmetric Maxwell equations
Author(s) -
Assous Franck,
Ciarlet Patrick,
Labrunie Simon
Publication year - 2003
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.400
Subject(s) - mathematics , sobolev space , gravitational singularity , mathematical analysis , maxwell's equations , rotational symmetry , space (punctuation) , geometry , philosophy , linguistics
In this article, we study the static and time‐dependent Maxwell equations in axisymmetric geometry. Using the mathematical tools introduced in ( Math. Meth. Appl. Sci. 2002; 25 : 49), we investigate the decoupled problems induced in a meridian half‐plane, and the splitting of the solution in a regular part and a singular part, the former being in the Sobolev space H 1 component‐wise. It is proven that the singular parts are related to singularities of Laplace‐like or wave‐like operators. We infer from these characterizations: (i) the finite dimension of the space of singular fields; (ii) global space and space–time regularity results for the electromagnetic field. This paper is the continuation of ( Modél. Math. Anal. Numér . 1998; 32 : 359, Math. Meth. Appl. Sci . 2002; 25 : 49). Copyright © 2003 John Wiley & Sons, Ltd.