Solution of searched function and its normal derivative jump problem for the Laplacian in R3 by means of simple and double layer potentials

Modeling of electrostatic fields at the environments with different characters leads to necessity of solution of the jump problems with inclined derivative for the Laplacian in R³. This problem at the Hilbert space the normal derivative elements of which has the jump through boundary surface was considered in [2]. Solution of this problem was searched as simple layer potential. At the Hilbert space the elements of which have the jump through boundary surface such problem was considered in [4]. Solution of this problem was searched as double layer potential. The searched function and its derivative jump problem at the Hilbert space elements of which as their normal derivatives has the jump through boundary surface are considered at this article. The conditions of well-posed solution of formulated problem 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.