Equicontinuity of the family of the open discrete Orlicz--Sobolev mappings

TL;DR

This paper studies the equicontinuity of open discrete Orlicz--Sobolev mappings with finite distortion, establishing their relation to ring $Q$-mappings and proving equicontinuity in higher dimensions.

Contribution

It demonstrates that open discrete lower ring $Q$-mappings are ring $Q^{n-1}$-mappings at fixed points, leading to new equicontinuity results for Orlicz--Sobolev mappings.

Findings

Open discrete lower ring $Q$-mappings are ring $Q^{n-1}$-mappings at fixed points

Equicontinuity of Orlicz--Sobolev mappings with finite distortion for $n \\ge 3$

Established connection between classes of ring $Q$-mappings and lower ring $Q$-mappings

Abstract

The paper is devoted to the study of mappings with non--bounded characteristics of quasiconformality. We investigate the interconnection between the classes of the so-called ring $Q$-mappings and lower ring $Q$-mappings. It is proved that open discrete lower ring $Q$-mappings are ring $Q^{n-1}$-mappings at fixed point. As consequence we obtain the equicontinuity of the class of the open discrete Orlicz--Sobolev mappings with finite distortion at $n\ge 3.$