Geodesic
Solution of the Neumann problem for the Laplace equation
Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 763-784

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For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.
Classification : 31B10, 35J05, 35J10, 35J25
Keywords: single layer potential; generalized normal derivative 
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     author = {Medkov\'a, Dagmar},
     title = {Solution of the {Neumann} problem for the {Laplace} equation},
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Medková, Dagmar. Solution of the Neumann problem for the Laplace equation. Czechoslovak Mathematical Journal, Tome 48 (1998) no. 4, pp. 763-784. http://geodesic.mathdoc.fr/item/CMJ_1998__48_4_a13/