Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 45, 2020, 259-277

ON MAPPINGS WHOSE INVERSES SATISFY THE POLETSKY INEQUALITY

Evgeny Sevost'yanov and Sergei Skvortsov

Zhytomyr Ivan Franko State University
40 Bol'shaya Berdichevskaya Str., 10 008 Zhytomyr, Ukraine
and Institute of Applied Mathematics and Mechanics of NAS of Ukraine
1 Dobrovol'skogo Str., 84 100 Slov'yans'k, Ukraine; esevostyanov2009 'at' gmail.com

Zhytomyr Ivan Franko State University
40 Bol'shaya Berdichevskaya Str., 10 008 Zhytomyr, Ukraine; serezha.skv 'at' gmail.com

Abstract. The article investigates mappings whose inverses distort the modulus of paths similarly to the Poletsky inequality. It is proved that the classes of such mappings form equicontinuous families if the majorant corresponding to the distortion of the module is integrable in the domain of their definition. Under additional conditions on the geometry of the domain of definition and the image domain these families are equicontinuous, not only at inner, but also at boundary points. In addition, the question of removability of the isolated singularities for such mappings is resolved.

2010 Mathematics Subject Classification: Primary 30C65; Secondary 32U20, 31B15.

Key words: Mappings with finite and bounded distortion, quasiconformal mappings, local and boundary behavior.

Reference to this article: E. Sevost'yanov and S. Skvortsov: On mappings whose inverses satisfy the Poletsky inequality. Ann. Acad. Sci. Fenn. Math. 45 (2020), 259-277.

Full document as PDF file

https://doi.org/10.5186/aasfm.2020.4520