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 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 when .
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}
}