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.
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Keywords: Diffeomorphic approximation, Ball-Evan’s, Sobolev homeomorphism
@article{COCV_2021__27_1_A28_0,
author = {Campbell, Daniel and Hencl, Stanislav},
title = {Approximation of planar {Sobolev} {\protect\emph{W}\protect\textsuperscript{2,1}} homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021019},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021019/}
}
TY - JOUR AU - Campbell, Daniel AU - Hencl, Stanislav TI - Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021019/ DO - 10.1051/cocv/2021019 LA - en ID - COCV_2021__27_1_A28_0 ER -
%0 Journal Article %A Campbell, Daniel %A Hencl, Stanislav %T Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021019/ %R 10.1051/cocv/2021019 %G en %F COCV_2021__27_1_A28_0
Campbell, Daniel; Hencl, Stanislav. Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 26. doi: 10.1051/cocv/2021019
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Cité par Sources :
The first author was supported by the grant GAČR 20-19018Y. The second author was supported by the grant GAČR P201/18-07996S.
