On multivalent solutions of the Riemann–Hilbert problem in multiply connected domains

TitleOn multivalent solutions of the Riemann–Hilbert problem in multiply connected domains
Publication TypeJournal Article
Year of Publication2016
AuthorsYefimushkin, AS
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
Date Published8/2016

For the Beltrami equations in the domains bounded by a finite collection of smooth Jordan curves, the existence of multivalent solutions of the Riemann–Hilbert problem with coefficients of sigma–finite variation and with boundary data, which are measurable with respect to the logarithmic capacity, is proved. It is shown that these spaces of solutions have the infinite dimension.

Keywordsanalytic functions, Beltrami equation, logarithmic capacity, multivalent solutions, Riemann–Hilbert problem
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