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Solution of the Dirichlet problem for the Laplace equation. (English) Zbl 1060.35041
Both classical and generalized solutions of the Dirichlet problem on open subset of \(\mathbb {R}^m\) with bounded cyclic variation are investigated. The solution is given in the form of a sum of the double layer potential and the single layer potential with the same density. The density is expressed in the form of the sum of a concrete series. In the case of the generalized solution the non-tangential limits of the solution are investigated.

MSC:
35J25 Boundary value problems for second-order elliptic equations
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35C15 Integral representations of solutions to PDEs
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