Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A\n Note

2020/11/06 by Armin Schikorra, James M. Scott, Schikorra, Armin +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2011.03198

openalex publication_date 2020/11/06 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

Let \Ω \⊂ \ℝⁿ be an open set and f_k \∈\nW^s,p(\Ω;\ℝⁿ) be a sequence of homeomorphisms weakly converging\nto f \∈ W^s,p(\Ω;\ℝⁿ). It is known that if s=1 and p >\nn-1 then f is injective almost everywhere in the domain and the target. In\nthis note we extend such results to the case s\∈(0,1) and sp > n-1. This\nin particular applies to C^s-H "older maps.\n

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