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The Beltrami equations and prime ends

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Abstract

We first study the boundary behavior of ring Q-homeomorphisms in terms of Carathéodory’s prime ends and then give criteria to the solvability of the Dirichlet problem for the degenerate Beltrami equation \( \overline{\partial} \) f = μ∂f in arbitrary bounded finitely connected domains D of the complex plane ℂ.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, NAS of Ukraine, Slavyansk, 84100, Ukraine

    Vladimir Gutlyanskii & Vladimir Ryazanov

  2. Holon Institute of Technology, Holon, Israel

    Eduard Yakubov

Authors
  1. Vladimir Gutlyanskii
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  2. Vladimir Ryazanov
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  3. Eduard Yakubov
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Correspondence to Vladimir Gutlyanskii.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 1, pp. 27–66, January–February, 2015.

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Gutlyanskii, V., Ryazanov, V. & Yakubov, E. The Beltrami equations and prime ends. J Math Sci 210, 22–51 (2015). https://doi.org/10.1007/s10958-015-2546-7

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