Approximation of W1,p Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian
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
Julkaistu sarjassa
Advances in MathematicsPäivämäärä
2018Tekijänoikeudet
© 2018 Elsevier Inc.
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 .
Julkaisija
Elsevier Inc.ISSN Hae Julkaisufoorumista
0001-8708Asiasanat
Katso myös
http://urn.fi/URN:NBN:fi:jyu-201611184661Julkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/28081817
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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.Lisenssi
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