On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909045359640576 |
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| author | Kovba, Zarina Sevost'yanov, Evgeny |
| author_facet | Kovba, Zarina Sevost'yanov, Evgeny |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15026 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes Kovba, Zarina Sevost'yanov, Evgeny Complex Variables 30C65 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. |
| title | On Caratheodory prime ends extension for unclosed Orlicz-Sobolev classes |
| topic | Complex Variables 30C65 |
| url | https://arxiv.org/abs/2604.15026 |