Differentiability almost everywhere of weak limits of bi-Sobolev homeomorphisms

2023/02/15 by A. DOLEŽALOVÁ, Doležalová, Anna, Anastasia Molchanova +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #46E35 #Bone Metabolism and Diseases #Cell Adhesion Molecules Research #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2302.07578

openalex publication_date 2023/02/15 · openalex created_date 2023/02/18 · openalex updated_date 2026/07/28

Abstract

This paper investigates the differentiability of weak limits of bi-Sobolev homeomorphisms. Given p>n-1, consider a sequence of homeomorphisms f_k with positive Jacobians J_fk >0 almost everywhere and sup_k(‖f_k‖_W^1,n-1 + ‖f_k^-1‖_W^1,p) <∞. We prove that if f and h are weak limits of f_k and f_k^-1, respectively, with positive Jacobians J_f>0 and J_h>0 a.e., then h(f(x))=x and f(h(y))=y both hold a.e. and f and h are differentiable almost everywhere.

Related

• Injectivity almost everywhere for weak limits of Sobolev homeomorphisms
• The weak and strong closures of Sobolev homeomorphisms are the same
• Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A\n Note
• Weak limit of homeomorphisms in W^1,n-1 and (INV) condition
• Jacobians of W^1,p homeomorphisms, case p=[n/2]