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An integral equation solution of the Dirichlet and Neumann problems for the Laplacian in R/sup 3/

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

The Dirichlet and Neumann boundary value problems for the Laplacian in R/sup 3/ at the Hilbert space, the elements of which as well as their normal derivatives have the jump through boundary surface, are considered in an article. The conditions of well-posed solution of the formulated problems are determined. We suggest to look for the solution of these problems as the sum of the simple and double layer potentials. Integral equations equivalent to the above mentioned boundary value problems are the equations of the first kind. We define the conditions of the well-posed solution of the latter.

Published in:

Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, 2003. DIPED 2003. Proceedings of 8th International Seminar/Workshop on

Date of Conference:

23-25 Sept. 2003