TY - JOUR
AU - Bouchala, Ondřej
AU - Hencl, Stanislav
AU - Zhu, Zheng
PY - 2024/09/13
Y2 - 2024/10/06
TI - Weak limit of W^1,2 homeomorphisms in R^3 can have any degree
JF - Annales Fennici Mathematici
JA - Ann. Fenn. Math.
VL - 49
IS - 2
SE - Articles
DO - 10.54330/afm.147887
UR - https://afm.journal.fi/article/view/147887
SP - 547–560
AB - <pre>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.</pre><p> </p>
ER -