Geodesic
The successive approximation method for the Dirichlet problem in a planar domain
Dagmar Medková1
1 Mathematical Institute Academy of Sciences of the Czech Republic Žitná 25 115 67 Praha 1, Czech Republic
Applicationes Mathematicae, Tome 35 (2008) no. 2, pp. 177-192.

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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.
DOI : 10.4064/am35-2-4
Keywords: dirichlet problem laplace equation planar domain piecewise smooth boundary studied using indirect integral equation method domain bounded unbounded supposed boundary connected boundary conditions continuous p integrable functions proved solution corresponding integral equation obtained using successive approximation method

Dagmar Medková 1

1 Mathematical Institute Academy of Sciences of the Czech Republic Žitná 25 115 67 Praha 1, Czech Republic 
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Dagmar Medková. The successive approximation method
 for the Dirichlet problem in a planar domain. Applicationes Mathematicae, Tome 35 (2008) no. 2, pp. 177-192. doi : 10.4064/am35-2-4. http://geodesic.mathdoc.fr/articles/10.4064/am35-2-4/

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