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A method for solving boundary value problems for the Laplace equation in domains with curvilinear boundary. (Russian) Zbl 0617.31001

The authors look for a harmonic function u in a simply connected bounded domain \(g\subset {\mathbb{R}}^ 2\) of certain class when on one part of the boundary \(u=0\), on another part \(\partial u/\partial \nu =0\) and on the supplement \(\Gamma\subset \partial G\) to these parts \(u=h\), where \(h\in L_ 2(\Gamma)\) is a given function. Sufficient conditions for the existence and uniqueness of a solution of this problem are given and a method for approximate solving is considered. This method was formerly applied by the authors to some problems of mechanics.
Reviewer: Ya.Rojtberg

MSC:

31A25 Boundary value and inverse problems for harmonic functions in two dimensions
31A20 Boundary behavior (theorems of Fatou type, etc.) of harmonic functions in two dimensions
31A05 Harmonic, subharmonic, superharmonic functions in two dimensions
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