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Symposium “Analysis on Manifolds with Singularities”, Breitenbrunn 1990 pp 43–50Cite as

A Collocation Method for a Screen Problem in ℝ3

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Part of the book series: Teubner-Texte zur Mathematik ((TTZM,volume 131))

Abstract

Let Ω: = (−1,1) × (−1,1) ⊂ ℝ2. The first kind integral equation on Ω,

$$ Vu\left( x \right): = \frac{1} {{4\pi }}\int\limits_\Omega {u\left( y \right)\frac{{dy}} {{\left| {x - y} \right|}} = f\left( x \right)\quad \left( {x \in \Omega } \right)} $$
(1.1)

gives the solution of the Dirichlet problem for the Laplace equation in ℝ3\Ω̄ with Dirichlet data f given on Ω, (“screen problem”) (see [6], [16]).

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293, D-6900, Heidelberg, Germany

    Martin Costabel

  2. Fachbereich Mathematik, Technische Hochschule Darmstadt, Schloßgartenstraße 7, D-6100, Darmstadt, Germany

    Frank Penzel & Reinhold Schneider

Authors
  1. Martin Costabel
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  2. Frank Penzel
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  3. Reinhold Schneider
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Editor information

Editors and Affiliations

  1. Jena, Germany

    Hans Triebel

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© 1992 Springer Fachmedien Wiesbaden

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Costabel, M., Penzel, F., Schneider, R. (1992). A Collocation Method for a Screen Problem in ℝ3 . In: Schulze, BW., Triebel, H. (eds) Symposium “Analysis on Manifolds with Singularities”, Breitenbrunn 1990. Teubner-Texte zur Mathematik, vol 131. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-11577-9_4

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  • DOI: https://doi.org/10.1007/978-3-663-11577-9_4

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-663-11578-6

  • Online ISBN: 978-3-663-11577-9

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