We study the boundary behavior of regular solutions to the degenerate Beltrami equations with constraints of the integral type imposed on the coefficient.
Similar content being viewed by others
References
T. V. Lomako, “On the theory of convergence and compactness for Beltrami equations,” Ukr. Math. J., 63, No. 3, 341–349 (2011).
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).
T. Lomako and V. Ryazanov, “On a variational method for the Beltrami equations,” Ann. Univ. Bucharest. Ser. Math., 60, No. 2, 3–14 (2011).
V. Ya. Gutlyanskii and V. I. Ryazanov, “On asymptotically conformal curves,” Complex Variables, 25, 357–366 (1994).
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).
V. Ya. Gutlyanskii and V. I. Ryazanov, Geometric and Topological Theory of Functions and Mappings [in Russian], Kiev, Naukova Dumka (2011).
E. A. Sevost’yanov, “On the boundary behavior of open discrete mappings with unbounded characteristic,” Ukr. Math. J., 64, No. 6, 979–984 (2012).
E. A. Sevost’yanov, “On equicontinuous families of mappings without values in variable sets,” Ukr. Math. J., 66, No. 3, 404–414 (2014).
V. Gutlyanskii, V. Ryazanov, U. Srebro, and E. Yakubov, The Beltrami Equation: A Geometric Approach, Developments in Mathematics. V. 26, Springer, New York (2012).
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).
W. Rudin, Function Theory in Polydiscs. Math. Lect. Notes Ser., Benjamin, Inc., New-York–Amsterdam (1969).
P. P. Belinskii, General Properties of Quasiconformal Mappings [in Russian], Novosibirsk, Nauka (1974).
V. I. Ryazanov and E. A. Sevost’yanov, “Normal families of space mappings,” Sib. Elektron. Mat. Izv., 3, 216–231 (2006).
O. Martio, V. Ryazanov, U. Srebro, and E. Yakubov, Moduli in Modern Mapping Theory. Springer Monographs in Mathematics, Springer, New York (2009).
K. Kuratowski, Topology, 1, New York, Academic Press (1966).
J. Becker and Chr. Pommerenke, “Uber die quasikonforme Fortsetzung schlichten Funktionen,” Math. Z., 161, No. 1, 69–80 (1978).
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.
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).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 4, pp. 489–498, April, 2015.
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-015-1100-6