On unclosed mappings with Poletsky inequality
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913301114388480 |
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| author | Desyatka, Victoria Sevost'yanov, Evgeny |
| author_facet | Desyatka, Victoria Sevost'yanov, Evgeny |
| contents | The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion. We consider mappings of domains of the Euclidean space that satisfy weighted Poletsky inequality. Assume that, the definition domain is finitely connected on its boundary and, in addition, on the set of all points which are pre-images of the cluster set of this boundary. Then the specified mappings have a continuous boundary extension provided that the majorant in the Poletsky inequality satisfies some integral divergence condition, or has a finite mean oscillation at every boundary point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On unclosed mappings with Poletsky inequality Desyatka, Victoria Sevost'yanov, Evgeny Complex Variables 30C65, 31A15, 31B25 The manuscript is devoted to the boundary behavior of mappings with bounded and finite distortion. We consider mappings of domains of the Euclidean space that satisfy weighted Poletsky inequality. Assume that, the definition domain is finitely connected on its boundary and, in addition, on the set of all points which are pre-images of the cluster set of this boundary. Then the specified mappings have a continuous boundary extension provided that the majorant in the Poletsky inequality satisfies some integral divergence condition, or has a finite mean oscillation at every boundary point. |
| title | On unclosed mappings with Poletsky inequality |
| topic | Complex Variables 30C65, 31A15, 31B25 |
| url | https://arxiv.org/abs/2404.03859 |