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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Vydáno v:SIAM journal on mathematical analysis Ročník 8; číslo 3; s. 504 - 517
Hlavní autoři: González, R., Kress, R.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.05.1977
Témata:
Boundary value problems
Integral equations
ISSN:0036-1410, 1095-7154
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Abstract 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.
AbstractList 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.
Author Kress, R.
González, R.
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crossref_primary_10_1186_1687_2770_2013_54
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Cites_doi 10.1007/BF01220037
10.1017/S0308210500018047
10.1007/978-3-642-87773-5
10.1137/0122044
10.1007/BF00282316
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  publication-title: Proc. Roy. Soc. Edinburgh Sect. A
  doi: 10.1017/S0308210500018047
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SubjectTerms Boundary value problems
Integral equations
Title On the Treatment of a Dirichlet–Neumann Mixed Boundary Value Problem for Harmonic Functions by an Integral Equation Method
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