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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Veröffentlicht in:	Journal of mathematical analysis and applications 2001-10, Vol.262 (2), p.733-748
Hauptverfasser:	Steinbach, O., Wendland, W.L.
Format:	Artikel
Sprache:	eng
Schlagworte:	boundary integral equations Exact sciences and technology Integral equations Mathematical analysis Mathematics Neumann series Sciences and techniques of general use
Online-Zugang:	Volltext
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Zusammenfassung:	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