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arXiv · 2203.14002

On discrete boundary extension of mappings in terms of prime ends

Evgeny Sevost'yanov
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Abstract

We study mappings that satisfy the inverse Poletsky inequality in a domain of the Euclidean space. Under certain conditions on the definition and mapped domains, it is established that they have a continuous extension to the boundary in terms of prime ends if the majorant involved in the Poletsky inequality is integrable over spheres. Under some additional conditions, the extension mentioned above is discrete.

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Evgeny Sevost'yanov. 2022-03-26. On discrete boundary extension of mappings in terms of prime ends. https://arxiv.org/abs/2203.14002

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