On discrete boundary extension of mappings in terms of prime ends

2022/03/26 by Evgeny Sevost’yanov, Sevost'yanov, Evgeny
Environmental Science · Materials Science · Mathematics · #30C65 #30L10 #31A15 #31A20 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Scientific Research and Studies #Structural mechanics and materials

paper · pdf · doi:10.48550/arxiv.2203.14002

openalex publication_date 2022/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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