Extending Lipschitz mappings continuously
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F12%3A00422594" target="_blank" >RIV/67985840:_____/12:00422594 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/jaa-2012-0011" target="_blank" >http://dx.doi.org/10.1515/jaa-2012-0011</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/jaa-2012-0011" target="_blank" >10.1515/jaa-2012-0011</a>
Alternative languages
Result language
angličtina
Original language name
Extending Lipschitz mappings continuously
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Applied Analysis
ISSN
1425-6908
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
2
Country of publishing house
CH - SWITZERLAND
Number of pages
11
Pages from-to
167-177
UT code for WoS article
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EID of the result in the Scopus database
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