Solution of axisymmetric Maxwell equations

Franck Assous, Patrick Ciarlet, Simon Labrunie

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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).

Original languageEnglish
Pages (from-to)861-896
Number of pages36
JournalMathematical Methods in the Applied Sciences
Issue number10
StatePublished - Jul 2003
Externally publishedYes


  • Axisymmetry
  • Conical vertices
  • Hodge decomposition
  • Maxwell equations
  • Reentrant edges
  • Regularity of solutions
  • Singularities


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