Publication at Faculty of Mathematics and Physics |
2017
Abstract
We construct a Sobolev homeomorphisms F is an element of W-1,W-2((0,1)(4), R-4) which fails the 2-dimensional Lusin's condition on H-2-positively many hyperplanes, i.e. there exists C-1 subset of [0,1](2) with H-2(C-1) > 0, such that for each (z, w) is an element of C-1 there is a set A((z,w)) C [0,1](2) with H-2(A((z,w))) = 0 and H-2(F(A((z,w)) x {(z, w)})) > 0.