Regularity of the Inverse of a Planar Sobolev Homeomorphism

By S. Hencl, Pekka Koskela. 2006

154 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/403a8573fdaa83554bac8a334c6f203ff89a8861

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Lectures on Mappings of Finite Distortion (2014, background): “The results about the regularity of the inverse in the planar case were established by Hencl and Koskela [12] and they are the main content in the first chapter of the book.”
Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms (2011, background): “In fact, it turns out that the bi-Sobolev maps are the natural class in which studying the problem, since Hencl and Koskela [17] proved that if u ∈ W 1,1(Ω;R2) is a planar homeomorphism satisfying (1.4), then u−1 ∈ W 1,1(u(Ω);R2); in other words, every map which is not bi-Sobolev, at least for p = 1”
Existence of energy-minimal diffeomorphisms between doubly connected domains (2010, unknown): “For every homeomorphism g : Ω∗ onto −→ Ω with integrable distortion the inverse map f = g−1 : Ω onto −→ Ω∗ belongs to the Sobolev class W 1,2(Ω) and we have [10, 11, 20]”
Hopf Differentials and Smoothing Sobolev Homeomorphisms (2010, background): “Since the inverse of such a homeomorphism need not be in any Sobolev class [18], some difficulties are to be expected.”
Fracture Surfaces and the Regularity of Inverses for BV Deformations (2011, background): “Related results on the regularity of the inverse have appeared recently in [21,22, 25,23,12,20,19].”
Homeomorphisms of Bounded Variation (2007, unknown): “For this see [2].”
n-Harmonic Mappings Between Annuli (2011, background): “where h denotes the inverse of f , [12, 19, 20].”
A note on extremal mappings of finite distortion (2005, unknown): “Our approach is motivated by the recent results in [ 6 ].”
Deformations of Annuli with Smallest Mean Distortion (2010, background): “It has bounded variation but fails to be absolutely continuous on lines, see [10,11] for related questions and results.”