Solution of axisymmetric Maxwell equations

Franck Assous, Patrick Ciarlet Jr. and Simon Labrunie
Publication type:
Paper in peer-reviewed journals
Mathematical Methods in the Applied Sciences, vol. 26(10), pp. 861-896
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 H1 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.
    author={Franck Assous and Patrick Ciarlet and Simon Labrunie },
    title={Solution of axisymmetric Maxwell equations },
    doi={10.1002/mma.400 },
    journal={Mathematical Methods in the Applied Sciences },
    year={2003 },
    volume={26(10) },