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Solution of the Hilbert boundary value problem for a multiply connected domain. (English) Zbl 0818.30026
Let \(D= \overline\mathbb{C}\backslash \bigcup^ n_{k= 0} \overline D_ k\), where \(D_ k\) are mutually disjoined circles. The author considers, in the Hölder space the following problem: Find a function \(\Phi(z)\) analytic in \(D\), satisfying on \(\partial D_ k\) the boundary conditions \(\text{Re}\{\lambda_ k \Phi\}= f_ k\), \(k= 0,1,\dots, n\), where \(\lambda_ k\), \(f_ k\) are given functions. In the special case, the solution of the problem are given in explicit form.

30E25 Boundary value problems in the complex plane
45E05 Integral equations with kernels of Cauchy type
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