Singularities of electromagnetic fields in polyhedral domains

In this paper, we investigate the singular solutions of time-harmonic Maxwe ll equations in a domain which has edges and polyhedral corners. It is now well known that in the presence of non-convex edges, the solution fields ha ve no square integrable gradients in general and that the main singularitie s are the gradients of singular functions of the Laplace operator [4,5]. We show how this type of result can be derived from the classical Mellin anal ysis, and how this analysis leads to sharper results concerning the singula r parts which belong to H-1. For the singular functions, we exhibit simple and explicit formulas based on (generalized) Dirichlet and Neumann singular ities for the Laplace operator. These formulas are more explicit than the r esults announced in our note [10].