Frank Jochmann
The semistatic limit for Maxwell's equations in an exterior domain
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

35Q60 Equations of electromagnetic theory and optics

35L45 Initial value problems for hyperbolic systems of first-order PDE

35M10 PDE of mixed type

Abstract: This paper provides a $L^p$-theory for the Maxwell-system in the semistatic limit case in an exterior domain. The problem under consideration is of mixed type, since the possibly nonlinear electric conductivity vanishes on a certain subset of the domain. The solution is obtained from a singular perturbation of the full Maxwell-system including the displacement current.