Distances between classes of sphere-valued Sobolev maps

Haïm Brézis; Petru Mironescu; Itai Shafrir

doi:10.1016/j.crma.2016.05.001

Distances between classes of sphere-valued Sobolev maps

Haïm Brézis, Petru Mironescu, Itai Shafrir

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We introduce an equivalence relation on W^s,p(S^N;S^N) involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases, we even obtain exact formulas. Next we discuss related issues for W^1,p(Ω;S¹).

Original language	English (US)
Pages (from-to)	677-684
Number of pages	8
Journal	Comptes Rendus Mathematique
Volume	354
Issue number	7
DOIs	https://doi.org/10.1016/j.crma.2016.05.001
State	Published - Jul 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1016/j.crma.2016.05.001

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title = "Distances between classes of sphere-valued Sobolev maps",

abstract = "We introduce an equivalence relation on Ws,p(SN;SN) involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases, we even obtain exact formulas. Next we discuss related issues for W1,p(Ω;S1).",

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AU - Shafrir, Itai

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AB - We introduce an equivalence relation on Ws,p(SN;SN) involving the topological degree, and we evaluate the distances (in the usual sense and in the Hausdorff sense) between the equivalence classes. In some special cases, we even obtain exact formulas. Next we discuss related issues for W1,p(Ω;S1).

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Distances between classes of sphere-valued Sobolev maps

Abstract

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