%0 Journal Article %T Solution of axisymmetric Maxwell equations %+ Propagation des Ondes : Étude Mathématique et Simulation (POEMS) %A Assous, Franck %A Ciarlet, Patrick %A Labrunie, Simon %< avec comité de lecture %@ 0170-4214 %J Mathematical Methods in the Applied Sciences %I Wiley %V 26 %N 10 %P 861-896 %8 2003 %D 2003 %R 10.1002/mma.400Journal articles %X 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. %G English %L hal-00989564 %U https://ensta-paris.hal.science/hal-00989564 %~ ENSTA %~ CNRS %~ INRIA %~ INRIA-SACLAY %~ INRIA_TEST %~ TESTALAIN1 %~ UMA_ENSTA %~ INRIA2