Volume 27, 2021
|Number of page(s)||39|
|Published online||26 March 2021|
Approximation of planar Sobolev W2,1 homeomorphisms by piecewise quadratic homeomorphisms and diffeomorphisms*
Department of Mathematics, University of Hradec Králové,
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: firstname.lastname@example.org
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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