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On The Boundary Behavior of Regular Solutions of the Degenerate Beltrami Equations

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Ukrainian Mathematical Journal Aims and scope

We study the boundary behavior of regular solutions to the degenerate Beltrami equations with constraints of the integral type imposed on the coefficient.

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References

  1. T. V. Lomako, “On the theory of convergence and compactness for Beltrami equations,” Ukr. Math. J., 63, No. 3, 341–349 (2011).

    Article  MathSciNet  Google Scholar 

  2. V. Ya. Gutlyanskii, T. V. Lomako, and V. I. Ryazanov, “To the theory of variational method for Beltrami equations,” Ukr. Mat. Visn., 8, No. 4, 513–536 (2011); English translation: J. Math. Sci., 182, No. 1, 37–54 (2012).

  3. T. Lomako and V. Ryazanov, “On a variational method for the Beltrami equations,” Ann. Univ. Bucharest. Ser. Math., 60, No. 2, 3–14 (2011).

    Google Scholar 

  4. V. Ya. Gutlyanskii and V. I. Ryazanov, “On asymptotically conformal curves,” Complex Variables, 25, 357–366 (1994).

  5. V. Ya. Gutlyanskii and V. I. Ryazanov, “To the theory of local behavior of quasiconformal mappings,” Izv. RAN, Ser. Mat., 59, No. 3, 31–58 (1995).

  6. V. Ya. Gutlyanskii and V. I. Ryazanov, Geometric and Topological Theory of Functions and Mappings [in Russian], Kiev, Naukova Dumka (2011).

  7. E. A. Sevost’yanov, “On the boundary behavior of open discrete mappings with unbounded characteristic,” Ukr. Math. J., 64, No. 6, 979–984 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  8. E. A. Sevost’yanov, “On equicontinuous families of mappings without values in variable sets,” Ukr. Math. J., 66, No. 3, 404–414 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  9. V. Gutlyanskii, V. Ryazanov, U. Srebro, and E. Yakubov, The Beltrami Equation: A Geometric Approach, Developments in Mathematics. V. 26, Springer, New York (2012).

    Google Scholar 

  10. V. Gutlyanskii, V. Ryazanov, U. Srebro, and E. Yakubov, “On recent advances in the degenerate Beltrami equations,” Ukr. Mat. Vesn., 7, No. 4, 467–515 (2010).

    MathSciNet  Google Scholar 

  11. W. Rudin, Function Theory in Polydiscs. Math. Lect. Notes Ser., Benjamin, Inc., New-York–Amsterdam (1969).

  12. P. P. Belinskii, General Properties of Quasiconformal Mappings [in Russian], Novosibirsk, Nauka (1974).

    Google Scholar 

  13. V. I. Ryazanov and E. A. Sevost’yanov, “Normal families of space mappings,” Sib. Elektron. Mat. Izv., 3, 216–231 (2006).

    MathSciNet  MATH  Google Scholar 

  14. O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov, Moduli in Modern Mapping Theory. Springer Monographs in Mathematics, Springer, New York (2009).

  15. K. Kuratowski, Topology, 1, New York, Academic Press (1966).

  16. J. Becker and Chr. Pommerenke, “Uber die quasikonforme Fortsetzung schlichten Funktionen,” Math. Z., 161, No. 1, 69–80 (1978).

  17. E. Lindelöf, “Sur la repre’sentation conforme d’une aire simplement connexe sur l’aire d’un cercle,” Quatrie’me Congre’s des Mathe’maticiens Scandinaves, Stockholm (1916), pp. 59–90.

  18. V. Gutlyanskii, O. Martio, and V. Ryazanov, “On a theorem of Lindelöf,” Ann. Univ. Mariae Curie-Sklodowska. Sect. A, 65, No. 2, 45–51 (2011).

    MathSciNet  MATH  Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 4, pp. 489–498, April, 2015.

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Lomako, T.V. On The Boundary Behavior of Regular Solutions of the Degenerate Beltrami Equations. Ukr Math J 67, 552–563 (2015). https://doi.org/10.1007/s11253-015-1100-6

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  • DOI: https://doi.org/10.1007/s11253-015-1100-6

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