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