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Regularity of the inverse of a homeomorphism with finite inner distortion

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Abstract

Let f: Ω → f(Ω) ⊂ ℝn be a W 1,1-homeomorphism with L 1-integrable inner distortion. We show that finiteness of min{lip f (x), k f (x)}, for every x ∈ Ω\E, implies that f −1 ∈ W 1,n and has finite distortion, provided that the exceptional set E has σ-finite ℋ1-measure. Moreover, f has finite distortion, differentiable a.e. and the Jacobian J f > 0 a.e.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P. O. Box 35, FI-40014, Jyväskylä, Finland

    Chang Yu Guo

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  1. Chang Yu Guo
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Correspondence to Chang Yu Guo.

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Supported partially by the Academy of Finland (Grant No. 131477) and the Magnus Ehrnrooth foundation

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Guo, C.Y. Regularity of the inverse of a homeomorphism with finite inner distortion. Acta. Math. Sin.-English Ser. 30, 1999–2013 (2014). https://doi.org/10.1007/s10114-014-3619-0

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  • DOI: https://doi.org/10.1007/s10114-014-3619-0

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