Weak limit of W^1,2 homeomorphisms in R^3 can have any degree

Authors

  • Ondřej Bouchala Czech Technical University in Prague, Faculty of Information Technology
  • Stanislav Hencl Charles University, Department of Mathematical Analysis
  • Zheng Zhu Beihang University, School of Mathematical Sciences

Keywords:

Limits of Sobolev homeomorphisms, topological degree

Abstract

In this paper for every kZ we construct a sequence of weakly converging homeomorphisms hm:B(0,10)R3, hmh in W1,2(B(0,10)), such that hm(x)=x on B(0,10) and for every r(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.

 

Section
Articles

Published

2024-09-13

How to Cite

Bouchala, O., Hencl, S., & Zhu, Z. (2024). Weak limit of W^1,2 homeomorphisms in R^3 can have any degree. Annales Fennici Mathematici, 49(2), 547–560. https://doi.org/10.54330/afm.147887