On boundary behavior of mappings in terms of prime ends
Evgeny Sevost'yanov
TL;DR
This paper investigates the boundary behavior of mappings related to Sobolev and Orlicz--Sobolev classes in the plane and space, providing new theorems on their boundary properties.
Contribution
It introduces new theorems describing the boundary behavior of Sobolev and Orlicz--Sobolev mappings using prime ends, extending existing boundary analysis methods.
Findings
Theorems on boundary behavior of Sobolev mappings.
Results applicable to mappings in the plane and space.
Enhanced understanding of prime end boundary behavior.
Abstract
A boundary behavior of mappings, which are closely related with Sobolev and Orlicz--Sobolev classes in the plane and in the space, is investigated. There are obtained theorems on boundary behavior of classes mentioned above.
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Taxonomy
TopicsAnalytic and geometric function theory · Holomorphic and Operator Theory · Advanced Mathematical Modeling in Engineering