Sobolev homeomorphism that cannot be approximated by diffeomorphisms in $W^{1,1}$

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10314055" target="_blank" >RIV/00216208:11320/16:10314055 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s00205-015-0895-5" target="_blank" >http://dx.doi.org/10.1007/s00205-015-0895-5</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00205-015-0895-5" target="_blank" >10.1007/s00205-015-0895-5</a>

Result language
angličtina
Original language name
Sobolev homeomorphism that cannot be approximated by diffeomorphisms in $W^{1,1}$
Original language description
We construct a Sobolev homeomorphism in dimension $ngeq 4$, $fin W^{1,1}((0,1)^n,er^n)$ such that $J_f=det Df>0$ on a set of positive measure and $J_f<0$ on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) $f_k$ such that $f_kto f$ in $W^{1,1}_{loc}$.
Czech name
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Czech description
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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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Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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