Construction of W^{2,n}(Ω) function with gradient violating Lusin (N) condition
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10335163" target="_blank" >RIV/00216208:11320/16:10335163 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1002/mana.201500014" target="_blank" >http://dx.doi.org/10.1002/mana.201500014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1002/mana.201500014" target="_blank" >10.1002/mana.201500014</a>
Alternative languages
Result language
angličtina
Original language name
Construction of W^{2,n}(Ω) function with gradient violating Lusin (N) condition
Original language description
We construct the smooth function f, such that its derivative belongs to W^{1,n}((0,1)^n,R^n) and it maps a line onto the full unit square. This shows that a mapping which maps a set of zero measure onto the set of positive measure can be a gradient mapping.
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
<a href="/en/project/LL1203" target="_blank" >LL1203: Properties of functions and mappings in Sobolev spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematische Nachrichten
ISSN
0025-584X
e-ISSN
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Volume of the periodical
289
Issue of the periodical within the volume
8-9
Country of publishing house
DE - GERMANY
Number of pages
12
Pages from-to
1100-1111
UT code for WoS article
000377274800011
EID of the result in the Scopus database
2-s2.0-84949643800