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Strongly elliptic boundary integral equations for electromagnetic transmission problems

Published online by Cambridge University Press:  14 November 2011

Martin Costabel  and
Ernst P. Stephan
Martin Costabel
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstr. 7, 6100 Darmstadt, Germany
Ernst P. Stephan
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 330332, U.S.A.
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Synopsis

We study a boundary integral equation method for transmission problems for strongly elliptic differential operators, which yields a strongly elliptic system of pseudodifferential operators and which therefore can be used for numerical computations with Galerkin's procedure. The method is shown to work for the vector Helmholtz equation in ℝ3 with electromagnetic transmission conditions. We propose a slightly modified system of boundary values in order for the corresponding bilinear form to be coercive over H1. We analyse the boundary integral equations using the calculus of pseudodifferential operators. Here the concept of the principal symbol is used to derive existence and regularity results for the solution.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 109 , Issue 3-4 , 1988 , pp. 271 - 296
Copyright
Copyright © Royal Society of Edinburgh 1988

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