On equicontinuity of homeomorphisms of the Orlicz and Orlicz – Sobolev classes in the closure of a domain - Petrov, E. A.; Sevost'yanov, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We investigate the behavior of homeomorphisms of the Orlicz – Sobolev classes in the closure of a domain. The theoremson equicontinuity of the indicated classes are obtained in terms of the prime ends of regular domains. In particular, it isshown that indicated classes are equicontinuous in domains with certain restrictions imposed on their boundaries providedthat the corresponding inner dilatation of order p has a majorant of finite mean oscillation at every point. We also provetheorems on the (pointwise) equicontinuity of the analyzed classes in the case of locally connected boundaries.