Abstract
Byline: Haim Brezis (1,3,4), Petru Mironescu (2), Itai Shafrir (3) Keywords: Primary 58D15; Secondary 46E35 We introduce an equivalence relation on the space W.sup.1,1([OMEGA] S.sup.1)<![CDATA[ ]]>W1,1([OMEGA]I3/4S1)<![CDATA[ ]]> 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.sup.1,p([OMEGA] S.sup.1)<![CDATA[ ]]>W1,p([OMEGA]I3/4S1)<![CDATA[ ]]> when p>1<![CDATA[ ]]>p>1<![CDATA[ ]]>. Author Affiliation: (1) 0000 0004 1936 8796, grid.430387.b, Department of Mathematics, Hill Center, Busch Campus, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ, 08854, USA (2) 0000 0001 2150 7757, grid.7849.2, Institut Camille Jordan, Universite de Lyon, Universite Lyon 1, CNRS UMR 5208, Villeurbanne, 69622, France (3) 0000000121102151, grid.6451.6, Department of Mathematics, Technion - I.I.T., Haifa, 32 000, Israel (4) 0000000121102151, grid.6451.6, Department of Computer Science, Technion - I.I.T., Haifa, 32 000, Israel Article History: Registration Date: 16/12/2017 Received Date: 29/09/2017 Accepted Date: 08/12/2017 Online Date: 22/12/2017 Article note: Communicated by L. Ambrosio.