On the Treatment of a Dirichlet–Neumann Mixed Boundary Value Problem for Harmonic Functions by an Integral Equation Method

Using an approach which extends the well-known classical integral equation methods, we reduce a mixed boundary value problem for harmonic functions to a system consisting of two integral equations of the second kind. Existence is proved by the Fredholm alternative for compact operators. The integral...

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Bibliographic Details
Published in:	SIAM journal on mathematical analysis Vol. 8; no. 3; pp. 504 - 517
Main Authors:	González, R., Kress, R.
Format:	Journal Article
Language:	English
Published:	Philadelphia Society for Industrial and Applied Mathematics 01.05.1977
Subjects:	Boundary value problems Integral equations
ISSN:	0036-1410, 1095-7154
Online Access:	Get full text
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Summary:	Using an approach which extends the well-known classical integral equation methods, we reduce a mixed boundary value problem for harmonic functions to a system consisting of two integral equations of the second kind. Existence is proved by the Fredholm alternative for compact operators. The integral equations can be solved apptgximately by successive iterations. Further investigations are made on the spectrum of the boundary integral operator.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14
ISSN:	0036-1410 1095-7154
DOI:	10.1137/0508038