Bi-Sobolev homeomorphism with zero Jacobian almost everywhere

DOI10.1007/s00526-013-0669-6zbMath1304.26009OpenAlexW2167099646MaRDI QIDQ406670

Luigi D'Onofrio, Stanislav Hencl, Roberta Schiattarella

Publication date: 9 September 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-013-0669-6

zbMATH Keywords

measuresnull sets\(p\)-integrable mappingsSobolev homeomorphisms

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Implicit function theorems, Jacobians, transformations with several variables (26B10)

Related Items (14)

Approximation of \(W^{1,p}\) Sobolev homeomorphism by diffeomorphisms and the signs of the Jacobian ⋮ Grand Sobolev spaces and their applications in geometric function theory and PDEs ⋮ Some remarks on Sobolev and bi-Sobolev mappings ⋮ Sobolev homeomorphisms with gradients of low rank via laminates ⋮ Hausdorff measure of critical set for Luzin \(N\) condition ⋮ On the Luzin \(N\)-property and the uncertainty principle for Sobolev mappings ⋮ Regularity of the inverse of a homeomorphism with finite inner distortion ⋮ Bi-Sobolev homeomorphisms \(f\) with \(Df\) and \(Df^{-1}\) of low rank using laminates ⋮ Recent studies on Sobolev mappings ⋮ On the bi-Sobolev planar homeomorphisms and their approximation ⋮ Genericity of infinite entropy for maps with low regularity ⋮ A measure and orientation preserving homeomorphism with approximate Jacobian equal -1 almost everywhere ⋮ Jacobians of \(W^{1,p}\) homeomorphisms, case \(p=[n/2\)] ⋮ Sobolev homeomorphism that cannot be approximated by diffeomorphisms in \(W^{1,1}\)

Cites Work

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• Regularity of the inverse of a planar Sobolev homeomorphism
• On the total variations for the inverse of a BV-homeomorphism
• Anisotropic Sobolev homeomorphisms
• Lusin's condition (N) and mappings of the class W1, n.
• Change of variables formula under minimal assumptions
• Mappings of finite distortion: Condition \(N\)

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