@article{9165e391de6a4a15aed7f372f41d3d40,
title = "Distances between classes in W1 , 1(Ω ; S1)",
abstract = "We introduce an equivalence relation on the space W1 , 1(Ω ; S1) 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 W1 , p(Ω ; S1) when p> 1.",
keywords = "Primary 58D15, Secondary 46E35",
author = "Haim Brezis and Petru Mironescu and Itai Shafrir",
note = "Funding Information: Acknowledgements The first author (HB) was partially supported by NSF grant DMS-1207793. The second author (PM) was partially supported by the LABEX MILYON (ANR-10-LABX-0070) of Universit{\'e} de Lyon, within the program “Investissements d{\textquoteright}Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR). The third author (IS) was supported by the Israel Science Foundation (Grant No. 999/13). Publisher Copyright: {\textcopyright} 2017, Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2018",
month = feb,
day = "1",
doi = "10.1007/s00526-017-1280-z",
language = "English (US)",
volume = "57",
journal = "Calculus of Variations and Partial Differential Equations",
issn = "0944-2669",
publisher = "Springer New York",
number = "1",
}