On removability of isolated singularities of Orlicz-Sobolev classes with branching

2014/07/21 by Evgeny Sevost’yanov, Evgeny Sevost'yanov, Sevost'yanov, Evgeny
Mathematics · #30C65 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #math.CV #msc:30C65

paper · pdf · doi:10.48550/arxiv.1407.5665

15 pages, in Russian

openalex publication_date 2014/07/21 · arxiv created 2014/12/27 · arxiv updated 2014/12/30 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

A local behavior of closed open discrete mappings of Orlicz--Sobolev classes in \Bbb Rⁿ, n≥ 3, is studied. It is proved that, mappings mentioned above have continuous extension to isolated boundary point x₀ of a domain D∖\x₀\ whenever n-1 degree of its inner dilatation has FMO (finite mean oscillation) at the point and, besides that, limit sets of f at x₀ and ∂ D are disjoint. Another sufficient condition of possibility of continuous extension is a divergence of some integral

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