The successive approximation method for the Dirichlet problem in a planar domain

Volume 35 / 2008

Dagmar Medková Applicationes Mathematicae 35 (2008), 177-192 MSC: 31A10, 35J05, 35J25, 65N38. DOI: 10.4064/am35-2-4

Abstract

The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or $p$-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.

Authors

  • Dagmar MedkováMathematical Institute
    Academy of Sciences of the Czech Republic
    Žitná 25
    115 67 Praha 1, Czech Republic
    e-mail

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