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

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1 Author(s)
Polishchuk, A.D. ; Inst. of Appl. Problems of Mech. & Math., NASU, Lviv, Ukraine

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.

Published in:

Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 2004. DIPED 2004. Proceedings of the 9th International Seminar/Workshop on

Date of Conference:

11-14 Oct. 2004