Solution of axisymmetric Maxwell equations
Franck Assous, Patrick Ciarlet, Simon Labrunie
Source abstract
Abstract 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.
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