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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.

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