Complete Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains

TL;DR

This paper thoroughly analyzes the low frequency behavior of solutions to time-harmonic generalized Maxwell equations in nonsmooth exterior domains, identifying degenerate operators and necessary solution components for accurate asymptotic description.

Contribution

It provides a complete characterization of low frequency asymptotics for Maxwell equations in nonsmooth domains, including the identification of degenerate operators and additional solution terms.

Findings

Identified degenerate operators in low frequency limit

Described the role of polynomially growing solutions in asymptotics

Extended the classical Neumann series to include additional solution components

Abstract

We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby, we identify degenerate operators in terms of special 'polynomially growing' solutions of a corresponding static problem, which must be added to the 'usual' Neumann series in order to describe the low frequency asymptotic adequately.