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On the Dirichlet problemfor the Beltrami equation

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Abstract

We show that homeomorphic W 1,1loc solutions of the Beltrami equations \(\overline \partial f = \mu \partial f\) satisfy certain modular inequalities. On this basis, we develop the theory of the boundary behavior of such solutions and prove a series of criteria for the existence of regular, pseudoregular and multi-valued solutions for the Dirichlet problem to the Beltrami equation in Jordan domains and finitely connected domains, respectively. These results have important applications to various problems of mathematical physics.

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Authors and Affiliations

  1. Institute of Appliedmathematics and Mechanics, National Academy of Sciences of Ukraine, 74 Roze Luxemburg Str., 83114, Donetsk, Ukraine

    D. Kovtonyuk, I. Petkov, V. Ryazanov & R. Salimov

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  1. D. Kovtonyuk
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  2. I. Petkov
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  3. V. Ryazanov
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  4. R. Salimov
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Correspondence to D. Kovtonyuk.

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Kovtonyuk, D., Petkov, I., Ryazanov, V. et al. On the Dirichlet problemfor the Beltrami equation. JAMA 122, 113–141 (2014). https://doi.org/10.1007/s11854-014-0005-x

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  • DOI: https://doi.org/10.1007/s11854-014-0005-x

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