\(C^{1}\) mappings in \(\mathbb{R}^5\) with derivative of rank at most 3 cannot be uniformly approximated by \(C^{2}\) mappings with derivative of rank at most 3

DOI10.1016/J.JMAA.2018.08.060zbMath1402.26008arXiv1804.08289OpenAlexW2963877088MaRDI QIDQ1791559

Paweł Goldstein, Piotr Hajłasz

Publication date: 10 October 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.08289

zbMATH Keywords

Sard's theoremapproximation by smooth mappingsrank of the derivative

Mathematics Subject Classification ID

Implicit function theorems, Jacobians, transformations with several variables (26B10) Approximation by other special function classes (41A30)

Related Items (2)

Smooth approximation of mappings with rank of the derivative at most 1 ⋮ Hausdorff measure of critical set for Luzin \(N\) condition

Cites Work

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• Mathematical analysis I. Translated from the 4th and 6th Russian editions by Roger Cooke and Octavio T. Paniagua
• Besicovitch-Federer projection theorem for continuously differentiable mappings having constant rank of the Jacobian matrix
• The measure of the critical values of differentiable maps

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