Extending Lipschitz mappings continuously

被引：6
|
作者：
Kopecka, Eva [1 ,2 ]
机构：
[1] Czech Acad Sci, Math Inst, Zitna 25, Prague 11567, Czech Republic
[2] Johannes Kepler Univ Linz, Inst Anal, A-4040 Linz, Austria
来源：
JOURNAL OF APPLIED ANALYSIS | 2012年 / 18卷 / 02期
关键词：
Lipschitz mapping; extension; Hilbert space;
D O I：
10.1515/jaa-2012-0011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider short mappings from a bounded subset of a Euclidean space into that space, that is, mappings which do not increase distances between points. By Kirszbraun's theorem any such mapping can be extended to the entire space to be short again. In general, the extension is not unique. We show that there are single-valued extension operators continuous in the supremum norm. The multivalued extension operator is lower semicontinuous.
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页码：167 / 177
页数：11
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