Weak limit of W^1,2 homeomorphisms in R^3 can have any degree

Abstrakti

In this paper for every $k\in \mathbb{Z}$ we construct a sequence of weakly converging homeomorphisms $h_m:B(0,10)\to {\mathbb{R}}^3$, $h_m\rightharpoonup h$ in $W^{1,2}(B(0,10))$, such that $h_m(x)=x$ on $\partial B(0,10)$ and for every $r\in (5/16,7/16)$ the degree of $h$ with respect to the ball $B(0,r)$ is equal to $k$ on a set of positive measure.