Archive for Rational Mechanics and Analysis

, Volume 180, Issue 1, pp 75–95 | Cite as

Regularity of the Inverse of a Planar Sobolev Homeomorphism

  • Stanislav Hencl
  • Pekka KoskelaEmail author


Let Open image in new window be a domain. Suppose that fW1,1loc(Ω,R2) is a homeomorphism such that Df(x) vanishes almost everywhere in the zero set of J f . We show that f-1W1,1loc(f(Ω),R2) and that Df−1(y) vanishes almost everywhere in the zero set of Open image in new window Sharp conditions to quarantee that f−1W1, q (f(Ω),R2) for some 1<q≤2 are also given.


Neural Network Complex System Nonlinear Dynamics Electromagnetism Sharp Condition 


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of JyväskyläJyväskyläFinland

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