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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.