Modulus of continuity of orientation preserving approximately\n differentiable homeomorphisms with a.e. negative Jacobian

2017/01/16 by Paweł Goldstein, Piotr Hajłasz, Goldstein, Paweł +1
Engineering · Immunology and Microbiology · Mathematics · #26B10 #26B35 #74B20 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Control and Dynamics of Mobile Robots #FOS: Mathematics #Macrophage Migration Inhibitory Factor #Primary 46E35 #Secondary 26B05

paper · pdf · doi:10.48550/arxiv.1701.04348

openalex publication_date 2017/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We construct an a.e. approximately differentiable homeomorphism of a unit\nn-dimensional cube onto itself which is orientation preserving, has the Lusin\nproperty (N) and has the Jacobian determinant negative a.e. Moreover, the\nhomeomorphism together with its inverse satisfy a rather general sub-Lipschitz\ncondition, in particular it can be bi-H "older continuous with an arbitrary\nexponent less than 1.\n

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