Filomat 2022 Volume 36, Issue 16, Pages: 5359-5390
https://doi.org/10.2298/FIL2216359M
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Hölder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings
Mateljević Miodrag 
(University of Belgrade, Faculty of Mathematics, Belgrade, Serbia), miodrag@matf.bg.ac.rs
Salimov Ruslan (Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine), ruslan.salimov1@gmail.com
Sevost’yanov Evgeny (Zhytomyr Ivan Franko State University, Zhytomyr, Ukraine + Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Slov’yans’k, Ukraine), esevostyanov2009@gmail.com
In this article, we consider the Hölder continuity of injective maps in
Orlicz-Sobolev classes defined on the unit ball. Under certain conditions on
the growth of dilatations, we obtain the Hölder continuity of the indicated
class of mappings. In particular, under certain special restrictions, we
show that Lipschitz continuity of mappings holds. We also consider Hölder
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
Hölder continuous.
Keywords: Quasiconformal mappings, Hölder and Lipschitz continuity, harmonic mappings
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