Distances between classes of sphere-valued Sobolev maps
Haïm Brézis, Petru Mironescu, Itai Shafrir · Comptes Rendus Mathématique · 2016
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 ; S 1 ) .