On the Hilbert problem for analytic functions in quasihyperbolic domains

1Gutlyanskii, VYa., 1Ryazanov, VI, 2Yakubov, E, 3Yefimushkin, AS
1Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Sloviansk
2Holon Institute of Technology, Israel
3Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 2:23-30
Section: Mathematics
Language: English

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.

Keywords: analytic and harmonic functions, and Poincaré boundaryvalue problems, angular limits, Dirichlet, Hilbert, logarithmic capacity, Neumann, quasihyperbolic boundary condition

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