Equicontinuity of the family of the open discrete Orlicz--Sobolev 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 $n\ge 3.$

arXiv comment24 pages, in Russian