Geodesic
Solution of the Dirichlet problem with l^p boundary condition
Kragujevac Journal of Mathematics, Tome 31 (2008) no. 1
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The solution of the Dirichlet problem for the Laplace equation is looked for in the form of the sum of a single layer and a double layer potentials with the same density $f$. The original problem is reduced to the solving of the integral equation with an unknown density $f$. The solution $f$ of this integral equation is given by the Neumann series. 
@article{KJM_2008_31_1_a2,
     author = {Dagmar Medkov\'a},
     title = {Solution of the {Dirichlet} problem with l^p boundary condition},
     journal = {Kragujevac Journal of Mathematics},
     pages = {29 - 42},
     year = {2008},
     volume = {31},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/KJM_2008_31_1_a2/}
}
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Dagmar Medková. Solution of the Dirichlet problem with l^p boundary condition. Kragujevac Journal of Mathematics, Tome 31 (2008) no. 1. http://geodesic.mathdoc.fr/item/KJM_2008_31_1_a2/