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On the theory of the Beltrami equation

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Abstract

We study ring homeomorphisms and, on this basis, obtain a series of theorems on the existence of the so-called ring solutions for degenerate Beltrami equations. A general statement on the existence of solutions for the Beltrami equations that extends earlier results is formulated. In particular, we give new existence criteria for homeomorphic solutions f of the class W 1,1loc with f −1 ∈ W 1,2loc in terms of tangential dilatations and functions of finite mean oscillation. The ring solutions also satisfy additional capacity inequalities.

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    V. Ryazanov

  2. Technion Israel Institute of Technology, Haifa, Israel

    U. Srebro

  3. Holon Academic Institute of Technology, 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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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 11, pp. 1571–1583, November, 2006.

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Ryazanov, V., Srebro, U. & Yakubov, E. On the theory of the Beltrami equation. Ukr Math J 58, 1786–1798 (2006). https://doi.org/10.1007/s11253-006-0168-4

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  • DOI: https://doi.org/10.1007/s11253-006-0168-4

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