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Some interior and exterior boundary-value problems for the Helmholtz equation in a quadrant

Published online by Cambridge University Press:  14 November 2011

E. Meister ,
F. Penzel ,
F.-O. Speck  and
F. S. Teixeira
E. Meister
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, D-6100 Darmstadt, Germany
F. Penzel
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, D-6100 Darmstadt, Germany
F.-O. Speck
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, P-1096 Lisboa Codex, Portugal
F. S. Teixeira
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, P-1096 Lisboa Codex, Portugal
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Synopsis

The Dirichlet, Neumann and mixed boundary-value problems for the two-dimensional Helmholtz equation in the interior or exterior of a quadrant are considered in a Sobolev space setting. It is shown that the potential operators arising in the interior problems can be used to derive systems of boundary integral equations to the exterior problems, which can be solved explicitly.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 275 - 294
Copyright
Copyright © Royal Society of Edinburgh 1993

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