Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 147-170

MODULUS OF CONTINUITY OF ORIENTATION PRESERVING APPROXIMATELY DIFFERENTIABLE HOMEOMORPHISMS WITH A.E. NEGATIVE JACOBIAN

Pawel Goldstein and Piotr Hajlasz

University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Institute of Mathematics
Banacha 2, 02-097 Warsaw, Poland; goldie 'at' mimuw.edu.pl

University of Pittsburgh, Department of Mathematics
301 Thackeray Hall, Pittsburgh, PA 15260, U.S.A.; hajlasz 'at' pitt.edu

Abstract. We construct an a.e. approximately differentiable homeomorphism of a unit n-dimensional cube onto itself which is orientation preserving, has the Lusin property (N) and has the Jacobian determinant negative a.e. Moreover, the homeomorphism together with its inverse satisfy a rather general sub-Lipschitz condition, in particular it can be bi-Hölder continuous with an arbitrary exponent less than 1.

2010 Mathematics Subject Classification: Primary 46E35; Secondary 26B05, 26B10, 26B35, 74B20.

Key words: Approximately differentiable homeomorphisms, orientation preserving, Hölder condition, approximation.

Reference to this article: P. Goldstein and P. Hajlasz: Modulus of continuity of orientation preserving approximately differentiable homeomorphisms with a.e. negative Jacobian. Ann. Acad. Sci. Fenn. Math. 43 (2018), 147-170.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4333