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arXiv · 1606.01526

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

Haim Brezis·Petru Mironescu·Itai Shafrir
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Abstract

We introduce an equivalence relation on the space $W^{1,1}(\Omega;{\mathbb S}^1)$ 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 $W^{1,p}(\Omega;{\mathbb S}^1)$ when $p>1$.

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Haim Brezis, Petru Mironescu, Itai Shafrir. 2016-06-05. Distances between classes in $W^{1,1}(\Omega;{\mathbb S}^1)$. https://doi.org/10.1007/s00526-017-1280-z

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