WIAS Preprint No. 129, (1994)

Boundary integral equations for the biharmonic Dirichlet problem on nonsmooth domains


Authors

  • Khoromskij, Boris N.
  • Schmidt, Gunther

2010 Mathematics Subject Classification

  • 31A30 47G10 65N38

Keywords

  • biharmonic equation, nonsmooth curve, boundary integral operators, boundary integral equations

DOI

10.20347/WIAS.PREPRINT.129

Abstract

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi-Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer biharmonic potentials, of the Calderon projections and the Poincaré-Steklov operators for such domains are analysed. We derive direct boundary integral equations equivalent to the variational formulation of the problem.

Appeared in

  • J. Integral Equations Appl., 11 (1999), No. 2, pp. 217-253.

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