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Regularity of the Inverse of a Planar Sobolev Homeomorphism

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Abstract

Let be a domain. Suppose that f ∈ W1,1loc(Ω,R2) is a homeomorphism such that Df(x) vanishes almost everywhere in the zero set of J f . We show that f-1 ∈ W1,1loc(f(Ω),R2) and that Df−1(y) vanishes almost everywhere in the zero set of Sharp conditions to quarantee that f−1 ∈ W1,q(f(Ω),R2) for some 1<q≤2 are also given.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), FIN-40014, Jyväskylä, Finland

    Stanislav Hencl & Pekka Koskela

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  1. Stanislav Hencl
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  2. Pekka Koskela
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Correspondence to Pekka Koskela.

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Communicated by V. Šverák

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Hencl, S., Koskela, P. Regularity of the Inverse of a Planar Sobolev Homeomorphism. Arch. Rational Mech. Anal. 180, 75–95 (2006). https://doi.org/10.1007/s00205-005-0394-1

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