On C. Neumann's Method for Second-Order Elliptic Systems in Domains with Non-smooth Boundaries

In this paper we investigate the convergence of Carl Neumann's method for the solution of Dirichlet or Neumann boundary values for second-order elliptic problems in domains with non-smooth boundaries. We prove that 12I+K, where K is the double-layer potential, is a contraction in H1/2(Γ) when a...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2001-10, Vol.262 (2), p.733-748
Main Authors: Steinbach, O., Wendland, W.L.
Format: Article
Language:English
Subjects:
boundary integral equations
Exact sciences and technology
Integral equations
Mathematical analysis
Mathematics
Neumann series
Sciences and techniques of general use
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Summary:In this paper we investigate the convergence of Carl Neumann's method for the solution of Dirichlet or Neumann boundary values for second-order elliptic problems in domains with non-smooth boundaries. We prove that 12I+K, where K is the double-layer potential, is a contraction in H1/2(Γ) when an energy norm is used that is induced by the inverse of the single-layer potential.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2001.7615