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On ring solutions of Beltrami equations

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Abstract

Ring homeomorphisms are studied and then applied to an extension of the known Lehto existence theorem for degenerate Beltrami equations. On the basis of this extension, we establish a series of new general integral and measure conditions on the complex coefficient for the existence of ACL homeomorphic solutions. These criteria imply many of the known existence theorems as well as new results.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. Roze Luxemburg 74, 83114, Donetsk, Ukraine

    V. Ryazanov

  2. Technion-Israel Institute of Technology, 32000, Haifa, Israel

    U. Srebro

  3. Holon Academic Institute of Technology, 52 Golomb St., P.O. Box 305, 58102, Holon, Israel

    E. Yakubov

Authors
  1. V. Ryazanov
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  2. U. Srebro
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  3. E. Yakubov
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Dedicated to Fred Gehring on the occasion of his 80th birthday

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Ryazanov, V., Srebro, U. & Yakubov, E. On ring solutions of Beltrami equations. J. Anal. Math. 96, 117–150 (2005). https://doi.org/10.1007/BF02787826

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  • DOI: https://doi.org/10.1007/BF02787826

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