On equicontinuity of Orlicz--Sobolev class in s closure of a domain

2016/02/22 by Evgeny Sevost’yanov, Sevost'yanov, Evgeny
Computer Science · Mathematics · #30C65 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1602.06918

openalex publication_date 2016/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A behavior of homeomorphisms of Orlicz--Sobolev classes in a closure of a domain is investigated. There are obtained theorems about equicontinuity of classes mentioned above in terms of prime ends of regular domains. In particular, it is proved that above classes are equicontinuous in domains with some restrictions on it's boundaries provided that the corresponding inner dilatation of order p has a majorant of finite mean oscillation at every point.

Related

• On equicontinuity of Sobolev classes in domains with locally connected boundary
• On boundary behavior of mappings of Sobolev and Orlicz--Sobolev class
• On removability of isolated singularities of Orlicz-Sobolev classes with\n branching
• Convergence and compactness of the Sobolev mappings
• On boundary extension of unclosed Orlicz-Sobolev mappings