H\"{o}lder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings
Complex Variables
2022-08-05 v1
Abstract
In this article, we consider the H\"{o}lder continuity of injective maps in Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on the growth of dilatations, we obtain the H\"{o}lder continuity of the indicated class of mappings. In particular, under certain special restrictions, we show that Lipschitz continuity of mappings holds. We also consider H\"{o}lder and Lipschitz continuity of harmonic mappings and in particular of harmonic mappings in Orlicz-Sobolev classes. In addition in planar case, we show in some situations that the map is bi-Lipschitzian if Beltrami coefficient is H\"{o}lder continuous.
Keywords
Cite
@article{arxiv.2208.02551,
title = {H\"{o}lder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings},
author = {Miodrag Mateljević and Ruslan Salimov and Evgeny Sevost'Yanov},
journal= {arXiv preprint arXiv:2208.02551},
year = {2022}
}