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, axially symmetric domain Ω. The solutions are written as the orthogonal sum of a regular part within H¹ (Ω)³, and a singular part. We show that, like in the two-dimensional case, the singular part is related to the (axisymmetric) singular eigenfuctions of the Laplacian, and hence is of finite dimension.