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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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
Keywords
- Mapping of finite distortion
- mappings of finite inner distortion
- bi-Sobolev homeomorphism
- Condition N on a.e. sphere
- modulus of rectifiable surfaces