Boundary integral equations for the biharmonic Dirichlet problem on nonsmooth domains
- Khoromskij, Boris N.
- Schmidt, Gunther
2010 Mathematics Subject Classification
- 31A30 47G10 65N38
- biharmonic equation, nonsmooth curve, boundary integral operators, boundary integral equations
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.
- J. Integral Equations Appl., 11 (1999), No. 2, pp. 217-253.