Singularities of electromagnetic fields in polyhedral domains
The authors investigate the singular solutions of time-harmonic Maxwell 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 have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the Laplace operator. The authors show how this type of result can be derived from the classical Mellin analysis, and how this analysis leads to sharper results concerning the singular parts which belong to \(H^1\). For the singular functions, the authors exhibit simple and explicit formulas based on (generalized) Dirichlet and Neumann singularities for the Laplace operator.
singular solutions of time-harmonic Maxwell equations
Dirichlet and Neumann singularities for the Laplace operator
scientific article; zbMATH DE number 1441233