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arXiv · 2604.15026

On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes

Zarina Kovba·Evgeny Sevost'yanov
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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.

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Zarina Kovba, Evgeny Sevost'yanov. 2026-04-16. On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes. https://arxiv.org/abs/2604.15026

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