Intrinsic geometries and boundary values of differentiable functions. I
type: Item
instance of: scholarly article
title: Intrinsic geometries and boundary values of differentiable functions. I
zbMATH Open document ID: 0692.46025
DOI: 10.1007/BF00971373
published in: Siberian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let G be an arbitrary domain in \(R^ n\). The author introduces an (anisotropic) intrinsic distance in G. With the help of this distance he characterizes in {\S} 1 some function spaces of Lipschitz-Nikolskij- Sobolev type in G. In {\S} 2 he studies boundary values of functions belonging to these function spaces (when \(\partial G\) is smooth then these boundary values coincide with the usual boundary values). Of special interest is {\S} 3 in which the author studies the extension problem: How to construct a linear extension operator for the function spaces on G into the corresponding function spaces on \(R^ n\) (sufficient and necessary conditions generalizing known results).
reviewed by: Hans Triebel
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 4132885
zbMATH Keywords: Lipschitz spaces
zbMATH Keywords: Nikolskij spaces
zbMATH Keywords: anisotropic intrinsic distance
zbMATH Keywords: function spaces of Lipschitz-Nikolskij-Sobolev type
zbMATH Keywords: extension problem
zbMATH Keywords: construct a linear extension operator
author: S. K. Vodop'yanov
MaRDI profile type: Publication
cites work: Q5802809
cites work: Q3763087
cites work: Q5797644
cites work: Quasiconformal mappings and extendability of functions in Sobolev spaces
cites work: The trace of subsets of \(R^ n\) of Besov spaces in the general case
full work available at URL: https://doi.org/10.1007/bf00971373
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description: scientific article; zbMATH DE number 4132885