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arXiv · 2208.02551

H\"{o}lder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings

Miodrag Mateljević·Ruslan Salimov·Evgeny Sevost'Yanov
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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.

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Miodrag Mateljević, Ruslan Salimov, Evgeny Sevost'Yanov. 2022-08-04. H\"{o}lder and Lipschitz continuity in Orlicz-Sobolev classes, distortion and harmonic mappings. https://arxiv.org/abs/2208.02551

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