Distances between homotopy classes of $W^{s, p} ({\mathbb S}^N ; {\mathbb S}^N)$ - Archive ouverte HAL Access content directly
Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2016

Distances between homotopy classes of $W^{s, p} ({\mathbb S}^N ; {\mathbb S}^N)$

Abstract

We investigate the metric and Hausdorff distance between the homotopy classes of $W^{s,p} ({\mathbb S}^N ; {\mathbb S}^N)$. Except in some limiting cases, we obtain either the exact value or the order of magnitude of these distances. A striking phenomenon arises when $sp>N\ge 2$, when the metric distance has an upper bound independent of the classes, while the Hausdorff distance of two different classes is infinite. We present several open problems and evidence in their favor.
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Dates and versions

hal-01257581 , version 1 (17-01-2016)

Identifiers

  • HAL Id : hal-01257581 , version 1

Cite

Haim Brezis, Petru Mironescu, Itai Shafrir. Distances between homotopy classes of $W^{s, p} ({\mathbb S}^N ; {\mathbb S}^N)$. ESAIM: Control, Optimisation and Calculus of Variations, 2016, 22 (4), pp.1204-1235. ⟨hal-01257581⟩
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