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The boundary-value problems for Laplace equation and domains with nonsmooth boundary. (English) Zbl 0910.35038
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.
Reviewer: M.Kučera (Praha)

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
31B10 Integral representations, integral operators, integral equations methods in higher dimensions
35J25 Boundary value problems for second-order elliptic equations
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