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

Abstract

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. Review of results about well-posed conditions for these problems at the Hilbert space the normal derivative elements of which has the jump through boundary surface were made in [6] and at the Hilbert space the elements of which has the jump through boundary surface were given in [7]. The conditions of well-posed solution of the double-sided Dirichlet, Neumann, and Dirichlet-Neumann problems at the Hilbert space elements of which as their normal derivatives has the jump through boundary surface were determined in [5, 9].