Weak limits of fractional Sobolev homeomorphisms are almost injective
Volume 269 / 2023
Studia Mathematica 269 (2023), 241-260
MSC: Primary 46E35; Secondary 47H11.
DOI: 10.4064/sm201218-20-9
Published online: 17 November 2022
Abstract
Let be an open set and f_k \in W^{s,p}(\Omega ;\mathbb {R}^n) be a sequence of homeomorphisms weakly converging to f \in W^{s,p}(\Omega ;\mathbb {R}^n). It is known that if s=1 and p \gt n-1 then f is injective almost everywhere in the domain and the target. In this note we extend such results to the case s\in (0,1) and sp \gt n-1. This in particular applies to C^s-Hölder maps.