Geodesic
Weak limit of W^1,2 homeomorphisms in R^3 can have any degree
Ondřej Bouchala1 ; Stanislav Hencl2 ; Zheng Zhu3
1Czech Technical University in Prague, Faculty of Information Technology
2Charles University, Department of Mathematical Analysis
3Beihang University, School of Mathematical Sciences
Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 547–560

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In this paper for every $k\in\mathbb{Z}$ we construct a sequence of weakly converging homeomorphisms $h_m\colon B(0,10)\to\mathbb{R}^3$, $h_m\rightharpoonup h$ 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.  
DOI : 10.54330/afm.147887
Keywords: Limits of Sobolev homeomorphisms, topological degree

Ondřej Bouchala  1   ; Stanislav Hencl  2   ; Zheng Zhu  3

1 Czech Technical University in Prague, Faculty of Information Technology
2 Charles University, Department of Mathematical Analysis
3 Beihang University, School of Mathematical Sciences 
Ondřej Bouchala; Stanislav Hencl; Zheng Zhu. Weak limit of W^1,2 homeomorphisms in R^3 can have any degree. Annales Fennici Mathematici, Tome 49 (2024) no. 2, p. 547–560. doi: 10.54330/afm.147887
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     title = {Weak limit of {W^1,2} homeomorphisms in {R^3} can have any degree},
     journal = {Annales Fennici Mathematici},
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