Solution of double-sided problem with inclined derivative for the Laplacian in R3 by means of simple and double layer potentials

Modeling of electrostatic fields at the environments with different characters lead to necessity of solution of the various boundary value problems for the Laplacian in R³ . The double-sided problem with inclined derivative for the Laplacian in R³ at the Hilbert space the normal derivative elements of which has the jump through boundary surface was considered. Solution of this problem was searched as simple layer potential. At the Hilbert space the elements of which has the jump through boundary surface such problem was considered. Solution of this problem was searched as double layer potential. The double-sided problem with inclined derivative at the Hilbert space elements of which as their normal derivatives has the jump through boundary surface is considered at this paper. The conditions of well-posed solution of formulated problems are determined. We suggest to look for the solution of this problem as the sum of simple and double layer potentials. We define the conditions of the well-posed solution of the later.