| Issue |
ESAIM: COCV
Volume 27, 2021
|
|
|---|---|---|
| Article Number | 26 | |
| Number of page(s) | 39 | |
| DOI | https://doi.org/10.1051/cocv/2021019 | |
| Published online | 26 March 2021 | |
Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms*
1
Department of Mathematics, University of Hradec Králové,
Rokitanského 62,
500 03
Hradec Králové, Czech Republic.
2
Faculty of Economics, University of South Bohemia,
Studentská 13,
Ceské Budejovice, Czech Republic.
3
Department of Mathematical Analysis, Charles University,
Sokolovská 83,
186 00
Prague 8, Czech Republic.
** Corresponding author: daniel.campbell@uhk.cz
Received:
18
August
2020
Accepted:
8
February
2021
Given a Sobolev homeomorphism f ∈ W2,1 in the plane we find a piecewise quadratic homeomorphism that approximates it up to a set of ε measure. We show that this piecewise quadratic map can be approximated by diffeomorphisms in the W2,1 norm on this set.
Mathematics Subject Classification: 46E35
Key words: Diffeomorphic approximation / Ball-Evan’s / Sobolev homeomorphism
© EDP Sciences, SMAI 2021
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