Weak Limit of $W^{1,2}$ Homeomorphisms in $mathbb{R}^3$ Can Have Any Degree

Kavli Affiliate: Zheng Zhu

| First 5 Authors: Ondřej Bouchala, Stanislav Hencl, Zheng Zhu, ,

| Summary:

In this paper for every $kinmathbb{Z}$ we construct a sequence of weakly
converging homeomorphisms $h_mcolon B(0,10)tomathbb{R}^3$,
$h_mrightharpoonup h$ in $W^{1,2}(B(0,10))$, such that $h_m(x)=x$ on $partial
B(0,10)$ and for every $rin left(tfrac5{16},tfrac{7}{16}right)$ the degree
of $h$ with respect to the ball $B(0,r)$ is equal to $k$ on a set of positive
measure.

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