Solution of the Dirichlet problem for the Laplace equation. (Q1775162)

Both classical and generalized solutions of the Dirichlet problem on open subset of~\(\mathbb {R}^m\) with bounded cyclic variation are investigated. The solution is given in the form of a sum of the double layer potential and the single layer potential with the same density. The density is expressed in the form of the sum of a concrete series. In the case of the generalized solution the non-tangential limits of the solution are investigated.