Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 771-797

SOBOLEV HOMEOMORPHISMS IN W^1,k AND THE LUSIN'S CONDITION (N) ON k-DIMENSIONAL SUBSPACES

Stanislav Hencl and Aapo Kauranen

Charles University, Department of Mathematical Analysis
Sokolovská 83, 186 00 Prague 8, Czech Republic; hencl 'at' karlin.mff.cuni.cz

aapo.p.kauranen 'at' gmail.com

Abstract. We construct a Sobolev homeomorphisms F ∈ W^1,2((0,1)⁴,R⁴) which fails the 2-dimensional Lusin's condition on H²-positively many hyperplanes, i.e. there exists C₁ ⊂ [0,1]² with H²(C₁) > 0, such that for each (z,w) ∈ C₁ there is a set A_(z,w) ⊂ [0,1]² with H²(A_(z,w)) = 0 and H²(F(A_(z,w) × {(z,w)})) > 0.

2010 Mathematics Subject Classification: Primary 46E35.

Key words: Lusin's condition, Sobolev mapping.

Reference to this article: S. Hencl and A. Kauranen: Sobolev homeomorphisms in W^1,k and the Lusin's condition (N) on k-dimensional subspaces. Ann. Acad. Sci. Fenn. Math. 42 (2017), 771-797.

Full document as PDF file

https://doi.org/10.5186/aasfm.2017.4244

SOBOLEV HOMEOMORPHISMS IN W1,k AND THE LUSIN'S CONDITION (N) ON k-DIMENSIONAL SUBSPACES

Stanislav Hencl and Aapo Kauranen

SOBOLEV HOMEOMORPHISMS IN W^1,k AND THE LUSIN'S CONDITION (N) ON k-DIMENSIONAL SUBSPACES