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Zbl 0910.35038
Medková, Dagmar
The boundary-value problems for Laplace equation and domains with nonsmooth boundary. (English)
[J] Arch. Math., Brno 34, No.1, 173-181 (1998). ISSN 0044-8753; ISSN 1212-5059/e

The author gives a survey of her recent results concerning the Dirichlet, Neumann and Robin boundary value problem for the Laplace equation on general open sets with holes and nonsmooth boundary. The boundary is supposed to be nonvoid, compact and satisfies the assumption $\partial \Omega = \partial \overline \Omega $. The solutions of the Neumann and Robin problem are looked for in the form of a single layer potential, the solution of the Dirichlet problem in a general case is expressed as a sum of a single layer potential and a double layer potential. The measure, the potential of which is a solution of the problem under consideration is constructed.
[M.Kučera (Praha)]

MSC 2000:: *35J05 Laplace equation, etc.
31B10 Integral representations of harmonic functions (higher-dimensional)
35J25 Second order elliptic equations, boundary value problems

Keywords: double layer potential; Dirichlet problem; Neumann problem; Robin problem; domains with holes; single layer potential

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