The Beltrami equations and prime ends

• Published in: Український математичний вісник
• Date: 2015
• Main Authors: Gutlyanskii, V.Y., Ryazanov, V.I., Yakubov, E.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/124487
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The Beltrami equations and prime ends / V.Y. Gutlyanskii, V.I. Ryazanov, E. Yakubov // Український математичний вісник. — 2015. — Т. 12, № 1. — С. 27-66. — Бібліогр.: 53 назв. — англ.

We first study the boundary behavior of ring Q-homeomorphisms in terms of Carath´eodory’s prime ends and then give criteria to the solvability of the Dirichlet problem for the degenerate Beltrami equation ∂f = μ∂f in arbitrary bounded finitely connected domains D of the complex plane C: