Solution of searched function jump problem for the Laplacian in R³ by means of double layer potential

Modeling of electrostatic fields in environments with different characteristics leads to the necessity of solving jump boundary value problems for the Laplacian in R³. The normal derivative jump problem in Hilbert space, the normal derivative elements of which have the jump through the boundary surface, has been considered (Nedelec, J.C. and Planchard, J., 1973). The solution of this problem was searched as a simple layer potential. We consider the searched function jump problem in Hilbert space, elements of which have the jump through the boundary surface. The conditions for a well-posed solution of the formulated problem are determinated. We suggest looking for the solution of this problem as the double layer potential. We define the conditions for the well-posed solution of the latter.