On the regular solutions of the Riemann–Hilbert problem for the Beltrami equations

1Yefimushkin, AS
2Ryazanov, VI
1Institute of Mathematics of the NAS of Ukraine, Kyiv
2Institute of Applied Mathematics and Mechanics of the NAS of Ukraine, Sloviansk
Dopov. Nac. akad. nauk Ukr. 2014, 5:19-23
https://doi.org/10.15407/dopovidi2014.05.019
Section: Mathematics
Language: Russian
Abstract: 

For the non-degenerate Beltrami equations in a unit disk, the existence of regular solutions of the Riemann–Hilbert problem with coefficients of bounded variation and almost continuous boundary data is proved.

Keywords: Beltrami equations, Riemann–Hilbert problem
References: 

1. Hilbert D. Uber eine Anwendung der Integralgleichungen auf eine Probl ¨ em der Funktionentheorie. In: Verhandl. des III Int. Math. Kongr., Heidelberg, 1904. Leipzig: Teubner, 1905: 233–240.
2. Hilbert D. Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen. Leipzig: Teubner, 1912.
3. Vekua I. N. Generalized analytic functions. Moscow: Fizmatgiz, 1959 (in Russian).
4. Nosiro K. Limit sets. Moscow: Izd-vo inostr. lit., 1963 (in Russian).
5. Nevalinna R. Single-valued analytic functions. Moscow: OGIZ, 1941 (in Russian).
6. Adams D. R., Hedberg L. I. Function spaces and potential theory. Berlin: Springer, 1996. https://doi.org/10.1007/978-3-662-03282-4
7. Twomey J. B. Irish Math. Soc. Bull., 2006, No. 58: 81–91.
8. Lehto O., Virtanen K. J. Quasiconformal mappings in the plane. Berlin; Heidelberg: Springer, 1973. https://doi.org/10.1007/978-3-642-65513-5
9. Kusis P. Introduction to the theory of Hp spaces. Moscow: Mir, 1984 (in Russian).
10. Goluzin G. M. Geometric theory of functions of a complex variable. Moscow: Nauka, 1966 (in Russian).