On boundary behavior of mappings with two normalized conditions
Journal Title: Математичні Студії - Year 2018, Vol 49, Issue 2
Abstract
The paper is devoted to a study of mappings with finite distortion that have been recently actively investigated last time. We study the boundary behavior of mappings between two fixed domains in metric spaces, which satisfy some moduli estimates. We have proved that families of corresponding inverse mappings with two normalized conditions and integrable majorant are equicontinuous whenever the domain of the mappings has a weakly at boundary
Authors and Affiliations
E. O. Sevost’yanov, S. A. Skvortsov, N. S. Ilkevych
Keywords
Related Articles
- EP ID EP411769
- DOI 10.15330/ms.49.2.150-157
- Views 55
- Downloads 0
Prime ends in the Sobolev mapping theory on Riemann surfaces
We prove criteria for continuous and homeomorphic extension to the boundary of mappings with finite distortion between domains on the Riemann surfaces by prime ends of Caratheodory.
On belonging of entire Dirichlet series to a modified generalized convergence class
For entire Dirichlet series F(s)=∑+∞n=0anesλn we found conditions on an, λn and on positive functions α and β continuous increasing to +∞ on [0,+∞) are found, under which the condition ∫+∞σ01β(σ)α(1σlnM(σ,F))dσ≤+∞ is equ...
On functions that are continuous on differentiable curves (in Ukrainian)
We prove that for a normed space X, a topological space Y, a point x0∈X, and a mapping f:X→Y, the continuity of all compositions f∘ω:[0,1]→Y at zero on differentiable curves ω:[0,1]→X with ω(0)=x0 yields the continuity o...
On a Banach space of Laplace-Stieltjes integrals
Let Ω be class of positive unbounded functions Φ on (−∞,+∞) such that the derivative Φ′ is positive, continuously differentiable and increasing to +∞ on (−∞,+∞), φ be the inverse function to Φ′, and Ψ(x)=x−Φ(x)Φ′(x) be t...
On one variational problem reducing to differential-boundary operator
One quadratic functional in the real space L2(Ω)(Ω⊂R2) is considered. The conditions are being necessary for the finding of its minimum are indicated and the problem of finding of corresponding sufficient conditions is f...