Distances between homotopy classes of $W^{s, p} ({\mathbb S}^N ; {\mathbb S}^N)$
Résumé
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.
Domaines
Analyse classique [math.CA]
Origine : Fichiers produits par l'(les) auteur(s)
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