On boundary distortion estimates of plane Sobolev mappings

Authors

  • E.O. Sevost'yanov Zhytomyr Ivan Franko State University, 40 Velyka Berdychivs'ka str., 10008, Zhytomyr, Ukraine https://orcid.org/0000-0001-7892-6186
  • N.S. Ilkevych Zhytomyr Ivan Franko State University, 40 Velyka Berdychivs'ka str., 10008, Zhytomyr, Ukraine https://orcid.org/0000-0003-0999-2299
  • V.S. Desyatka Zhytomyr Ivan Franko State University, 40 Velyka Berdychivs'ka str., 10008, Zhytomyr, Ukraine
https://doi.org/10.15330/cmp.18.1.117-134

Keywords:

quasiconformal mapping, mapping with finite distortion, Sobolev mapping, Hölder continuity, Lipschitz continuity
Published online: 2026-05-24

Abstract

We study mappings of the Sobolev classes defined in some plane domain. We have obtained estimates of the distortion of the distance under these mappings at the boundary. In particular, we have proved that if the integral averages of the characteristic of mappings are finite, then these mappings are Hölder continuous.

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How to Cite
(1)
Sevost'yanov, E.; Ilkevych, N.; Desyatka, V. On Boundary Distortion Estimates of Plane Sobolev Mappings. Carpathian Math. Publ. 2026, 18, 117-134.