Geodesic
On the global behavior of inverse mappings in terms of prime ends
Nataliya Ilkevych1 ; Evgeny Sevost'yanov2 ; Sergei Skvortsov1
1Zhytomyr Ivan Franko State University
2Zhytomyr Ivan Franko State University and Institute of Applied Mathematics and Mechanics of NAS of Ukraine
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 371-388
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The paper is devoted to the study of mappings with finite distortion, actively studied recently. For mappings whose inverse satisfy the Poletsky inequality, the results on boundary behavior in terms of prime ends are obtained. In particular, it was proved that the families of the indicated mappings are equicontinuous at the points of the boundary if a certain function determining the distortion of the modulus of families of paths under the mappings is integrable.
Keywords: Mappings with a finite and bounded distortion, boundary behaviour, prime ends

Nataliya Ilkevych  1   ; Evgeny Sevost'yanov  2   ; Sergei Skvortsov  1

1 Zhytomyr Ivan Franko State University
2 Zhytomyr Ivan Franko State University and Institute of Applied Mathematics and Mechanics of NAS of Ukraine 
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Nataliya Ilkevych; Evgeny Sevost'yanov; Sergei Skvortsov. On the global behavior of inverse mappings in terms of prime ends. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 371-388. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a20/