English

Distances between classes in $W^{1,1}(\Omega;{\mathbb S}^1)$

Functional Analysis 2018-01-03 v3

Abstract

We introduce an equivalence relation on the space W1,1(Ω;S1)W^{1,1}(\Omega;{\mathbb S}^1) which classifies maps according to their "topological singularities". We establish sharp bounds for the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. Similar questions are examined for the space W1,p(Ω;S1)W^{1,p}(\Omega;{\mathbb S}^1) when p>1p>1.

Keywords

Cite

@article{arxiv.1606.01526,
  title  = {Distances between classes in $W^{1,1}(\Omega;{\mathbb S}^1)$},
  author = {Haim Brezis and Petru Mironescu and Itai Shafrir},
  journal= {arXiv preprint arXiv:1606.01526},
  year   = {2018}
}
R2 v1 2026-06-22T14:18:07.568Z