On convergence and normality theorems of local homeomorphisms of Orlicz-Sobolev classes

Abstract

There are investigated problems connected with local and boundary properties of Orlicz--Sobolev classes of finite distortion which are actively studied last time. It is showed that, a locally uniform limit of local homeomorphisms of Orlicz--Sobolev class is a local homeomorphism or a constant whenever it's dilatations satisfy corresponding restrictions. Besides that, at some additional conditions, it is showed that, a locally uniform limit of the mappings mentioned above is a local homeomorphism or a constant.