Solution of Searched Function Jump Problem with Internal or External Dirichlet Condition for the Laplacian in R<sup>3</sup> by Means of Simple and Double Layer Potentials

Abstract

Modeling of electrostatic fields at the environments with different characters leads to necessity of solution of the jump boundary value problems for the Laplacian in R3. The searched function jump problem at the Hilbert space elements of which have the jump through boundary surface was considered in A. D. Polishchuk (2004). Solution of this problem was searched as double layer potential. At the Hilbert space elements of which as their normal derivatives have the jump through boundary surface only searched function jump condition is not sufficient for obtaining of searched function. We have to add to this condition additional internal or external Dirichlet condition and suggest to look for the solution of this problem the sum of simple and double layer potentials (A. D. Polishchuk, 2003).