A note on extremal mappings of finite distortion

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n-Harmonic Mappings Between Annuli (2011, background): “where h denotes the inverse of f , [12, 19, 20].”
Deformations of Annuli with Smallest Mean Distortion (2010, unknown): “This map has integrable distortion since ∫∫ Ω K(z, f̃ ) = ∞∑ j=1 ∫∫ Ω j K(z, f j ) ∫∫ Ω ′ ‖Dh‖2 Finally we appeal to the recent result of Hencl–Koskela–Onninen [12] which tells us that a homeomorphism f̃ : Ω → Ω ′ of integrable distortion in the Sobolev class W 1,1(Ω,Ω ′) has its inverse h̃ ∈ W 1,2(”
Regularity of the Inverse of a Planar Sobolev Homeomorphism (2006, methodology): “In [ 14 ], we show that the W 1,1 -minimizers of the L 1 -integral of a suitable distortion function are in fact smooth, with a harmonic inverse.”