On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes

Abstract

We study problems related to continuous boundary extension of mappings of Orlicz-Sobolev classes in terms of prime ends. The results we obtain concern the case when the mappings are open, discrete, but not closed (not preserving the boundary of a domain). These results generalize the well-known results of Caratheodory on boundary extension of conformal mappings.

arXiv admin note: substantial text overlap with arXiv:2504.18123