Weak limit of W^1,2 homeomorphisms in R^3 can have any degree
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.
Authors
- Zheng Zhu (ORCID: https://orcid.org/0000-0003-2543-473X)
- Stanislav Hencl
- Ondrěj Bouchala (ORCID: https://orcid.org/0000-0002-1348-2817)
Institutions
- Charles University (CZ)
- Department of Mathematical Sciences (RU)
- Czech Technical University in Prague (CZ)
- Beihang University (CN)
Publication Details
- Journal
- Annales Fennici Mathematici
- Published
- 2024-09-13
- DOI
- https://doi.org/10.54330/afm.147887
- Primary Topic
- Advanced Differential Equations and Dynamical Systems
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Univerzita Karlova v Praze
- National Natural Science Foundation of China