Singularities of electromagnetic fields in polyhedral domains
type: Item
instance of: scholarly article
title: Singularities of electromagnetic fields in polyhedral domains
zbMATH Open document ID: 0968.35113
author: Monique Dauge
author: Martin Costabel
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-09-18T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 78A25
zbMATH DE Number: 1441233
zbMATH Keywords: singular solutions of time-harmonic Maxwell equations
zbMATH Keywords: edges
zbMATH Keywords: corners
zbMATH Keywords: Mellin analysis
zbMATH Keywords: explicit formulas
zbMATH Keywords: Dirichlet and Neumann singularities for the Laplace operator
reviewed by: B. D. Sleeman
MaRDI profile type: Publication
full work available at URL: s002050050197
OpenAlex ID: W2000554621
DOI: 10.1007/S002050050197
description: scientific article; zbMATH DE number 1441233