Characterization of the singular part of the solution of steady-state Maxwell's equations in an axisymmetric domain

We study the steady-state Maxwell equations in a non-smooth, non-convex, ax ially symmetric domain Omega. The solutions are written as the orthogonal s um of a regular part within H-1(Omega)(3), and a singular part. We show tha t, like in the two-dimensional case, the singular part is related to the (a xisymmetric) singular eigenfuctions of the Laplacian, and hence is of finit e dimension. (C) Academie des Sciences/Elsevier, Paris.