Distances between classes in W^1,1(Ω ;\mathbb S¹) W 1 , 1 ( Ω ; S 1 )

2016/06/30 by Haïm Brézis, Haim Brezis, Petru Mironescu +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Topology and Set Theory #Combinatorics #Discrete mathematics #Equivalence (formal languages) #Equivalence relation #Gravitational singularity #Hausdorff space #Mathematical analysis #Mathematics #Nonlinear Partial Differential Equations #Omega #Physics #Space (punctuation) #math.FA

paper · pdf · doi:10.1007/s00526-017-1280-z

openalex created_date 2016/06/24 · arxiv created 2017/10/02 · openalex publication_date 2017/12/22 · arxiv updated 2018/01/03 · openalex updated_date 2026/08/06

Abstract

We introduce an equivalence relation on the space W^1,1(Ω;\mathbb 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 W^1,p(Ω;\mathbb S¹) when p>1.

Citations

• Optimal Transport
• Boundary regularity and the Dirichlet problem for harmonic maps
• Convexity conditions and existence theorems in nonlinear elasticity