Solution of the Dirichlet problem with l^p boundary condition

Dagmar Medková

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.