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On the Equivalence of two Transmission Boundary-Value Problems for the Time-Harmonic Maxwell Equations without Displacement Currents

  • We consider two transmission boundary-value problems for the time-harmonic Maxwell equations without displacement currents. For the first problem we use the continuity of the tangential parts of the electric and magnetic fields across material discontinuities as transmission conditions. In the second case the continuity of the tangential components of the electric field E is replaced by the continuity of the normal component of the magnetization B=müH. For this problem existence of solutions is already shown in [6]. If the domains under consideration are not simply connected the solution is not unique. In this paper, we improve the regularity results obtained in [6] and then prove existence and uniqueness theorems for the first problem by extracting its solution out of the set of all solutions of the second problem. Thus we establish a connection between the solutions corresponding to the different transmission boundary conditions.

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Author:Martin Reißel
Serie (Series number):Berichte der Arbeitsgruppe Technomathematik (AGTM Report) (86)
Document Type:Preprint
Language of publication:English
Year of Completion:1992
Year of Publication:1992
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/10/17
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011