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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:
 3e+26 Boundary value problems in the complex plane 4.5e+06 Integral equations with kernels of Cauchy type