The regularity of the inverses of Sobolev homeomorphisms with finite distortion

DOI10.1007/s12220-012-9345-xzbMath1300.26009OpenAlexW2012135387MaRDI QIDQ472016

Antonia Passarelli Di Napoli, Gioconda Moscariello

Publication date: 18 November 2014

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12220-012-9345-x

zbMATH Keywords

area formulabi-Sobolev mappingshomeomorphisms with finite distortion

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Integration of real functions of several variables: length, area, volume (26B15) Continuity and differentiation questions (26B05)

Related Items (14)

On the regularity theory of bi-Sobolev mappings ⋮ Bi-Sobolev mappings and \(K_{p}\)-distortions in the plane ⋮ Bi-Sobolev homeomorphisms and \(B^q_p\) classes ⋮ Grand Sobolev spaces and their applications in geometric function theory and PDEs ⋮ Bisobolev mappings and homeomorphisms with finite distortion ⋮ Absolute continuity in higher dimensions ⋮ Quasiconformal mappings and sharp estimates for the distance to \(L^\infty\) in some function spaces ⋮ A quantitative estimate for mappings of bounded inner distortion ⋮ Regularity of the inverse of a homeomorphism with finite inner distortion ⋮ Mappings of finite inner distortion: global homeomorphism theorem ⋮ Higher differentiability for \(n\)-harmonic systems with Sobolev coefficients ⋮ Recent studies on Sobolev mappings ⋮ On the approximate differentiability of inverse maps ⋮ Singularities in L^p-quasidisks

Cites Work

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• Sharpness of the assumptions for the regularity of a homeomorphism
• The limit of \(W^{1,1}\) homeomorphisms with finite distortion
• Bi-Sobolev mappings with differential matrices in Orlicz Zygmund classes
• Bi-Sobolev mappings and elliptic equations in the plane
• Differentiability of monotone Sobolev functions.
• Regularity of the inverse of a planar Sobolev homeomorphism
• Change of variables for absolutely continuous functions
• Higher integrability of determinants and weak convergence in L1.
• Homeomorphisms in the Sobolev space W 1,n–1
• Lusin's condition (N) and mappings of the class W1, n.
• Regularity of the inverse of a Sobolev homeomorphism in space
• Mappings of finite distortion: Condition \(N\)

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