Work

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

Year: 2024

Type: article

Abstract: 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.

Source: Annales Fennici Mathematici

DOI: 10.54330/afm.147887

Authors: Ondřej Bouchala, Stanislav Hencl, Zheng Zhu

Institutions: Czech Technical University in Prague, Charles University, Beihang University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Univerzita Karlova v Praze, National Natural Science Foundation of China

OpenAlex ID: W4402503920

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