On the Hilbert problem for analytic functions in quasihyperbolic domains
DOI:
https://doi.org/10.15407/dopovidi2019.02.023Keywords:
analytic and harmonic functions, and Poincaré boundaryvalue problems, angular limits, Dirichlet, Hilbert, logarithmic capacity, Neumann, quasihyperbolic boundary conditionAbstract
We study the Hilbert boundaryvalue problem for analytic functions in the Jordan domains satisfying the quasihyperbolic boundary condition by Gehring—Martio. Assuming that the coefficients of the problem are functions of the countably bounded variation and the boundary data are measurable with respect to the logarithmic capacity, we prove the existence of solutions of the problem in terms of angular limits. As consequences, we derive the corresponding results concerning the Dirichlet, Neumann, and Poincaré boundaryvalue problems for harmonic functions.
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