Geodesic
Weak limit of W^1,2 homeomorphisms in R^3 can have any degree
Ondřej Bouchala1 ; Stanislav Hencl2 ; Zheng Zhu3
1 Czech Technical University in Prague, Faculty of Information Technology
2 Charles University, Department of Mathematical Analysis
3 Beihang 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 
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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. http://geodesic.mathdoc.fr/articles/10.54330/afm.147887/

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