Characterization of the singular part of the solution of Maxwell's equations in a polyhedral domain
F. Assous, Patrick Ciarlet, Pierre-Arnaud Raviart, E. Sonnendrücker · Mathematical Methods in the Applied Sciences · 1999
The solution of Maxwell's equations in a non-convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian. Copyright © 1999 John Wiley & Sons, Ltd.