Geodesic
Solution of the Dirichlet problem for the Laplace equation
Applications of Mathematics, Tome 44 (1999) no. 2, pp. 143-168.

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For open sets with a piecewise smooth boundary it is shown that a solution of the Dirichlet problem for the Laplace equation can be expressed in the form of the sum of the single layer potential and the double layer potential with the same density, where this density is given by a concrete series.
DOI : 10.1023/A:1022209421576
Classification : 31B10, 35C15, 35J05, 35J25
Keywords: Laplace equation; Dirichlet problem; single layer potential; double layer potential 
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     title = {Solution of the {Dirichlet} problem for the {Laplace} equation},
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Medková, Dagmar. Solution of the Dirichlet problem for the Laplace equation. Applications of Mathematics, Tome 44 (1999) no. 2, pp. 143-168. doi : 10.1023/A:1022209421576. http://geodesic.mathdoc.fr/articles/10.1023/A:1022209421576/

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