HOLDER AND LIPSCHITZ CONTINUITY IN ORLICZ-SOBOLEV CLASSES, DISTORTION AND HARMONIC MAPPINGS

Abstract

In this article, we consider the Holder continuity of injective maps in Orlicz-Sobolev
classes dened on the unit ball. Under certain conditions on the growth of dilatations,
we obtain the Holder continuity of the indicated class of mappings. In particular, under
certain special restrictions, we show that Lipschitz continuity of mappings holds. We
also consider Holder 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 coecient is Holder
continuous.