Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
Abstract
Let Ω ⊂ R n, n ≥ 4, be a domain and 1 ≤ p < [n/2], where [a] stands for the integer part of a. We construct a homeomorphism f ∈ W1,p((−1, 1)n, R n) such that Jf = det Df > 0 on a set of positive measure and Jf < 0 on a set of positive measure. It follows that there are no diffeomorphisms (or piecewise affine homeomorphisms) fk such that fk → f in W1,p .
Main Authors
Format
Articles
Research article
Published
2018
Series
Subjects
Publication in research information system
Publisher
Elsevier Inc.
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-201904052076Use this for linking
Review status
Peer reviewed
ISSN
0001-8708
DOI
https://doi.org/10.1016/j.aim.2018.04.017
Please see also
http://urn.fi/URN:NBN:fi:jyu-201611184661
Language
English
Published in
Advances in Mathematics
Citation
- Campbell, D., Hencl, S., & Tengvall, V. (2018). Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian. Advances in Mathematics, 331, 748-829. https://doi.org/10.1016/j.aim.2018.04.017
License
Funder(s)
Research Council of Finland
Funding program(s)
Akatemiahanke, SA
Academy Project, AoF
Additional information about funding
All authors were supported by the ERC CZ grant LL1203 of the Czech Ministry of Education. V. Tengvall was also supported by the Vilho, Yrjö and Kalle Väisälä foundation and the Academy of Finland Project 277923.
Copyright© 2018 Elsevier Inc.