The Morse-Sard theorem for Sobolev spaces in a borderline case

DOI10.1016/j.bulsci.2010.02.001zbMath1251.46015OpenAlexW2055244278MaRDI QIDQ428770

Roberto van der Putten

Publication date: 25 June 2012

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2010.02.001

zbMATH Keywords

Sobolev spacecapacityPoincaré inequalityMorse-Sard theorem

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Inequalities involving derivatives and differential and integral operators (26D10) Hausdorff and packing measures (28A78) Potentials and capacities, extremal length and related notions in higher dimensions (31B15)

Related Items (3)

A bridge between Dubovitskiĭ-Federer theorems and the coarea formula ⋮ The generalized Morse-Sard theorem ⋮ The Morse-Sard theorem in \(W^{n,n} (\Omega)\): A simple proof

Cites Work

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• Traces of Sobolev functions on fractal type sets and characterization of extension domains
• Images of critical sets
• The Zygmund Morse-Sard theorem
• Lectures on analysis on metric spaces
• Sobolev spaces on an arbitrary metric space
• Sard's theorem for mappings in Hölder and Sobolev spaces
• A simple proof of the Morse-Sard theorem in Sobolev spaces
• A Critical Set with Nonnull Image has Large Hausdorff Dimension
• On the Image Size of Singular Maps. I
• Weakly Differentiable Functions
• Toward a Precise Smoothness Hypothesis in Sard's Theorem
• Lusin's condition (N) and mappings of the class W1, n.
• Pointwise inequalities for Sobolev functions revisited
• Morse-Sard theorem in Sobolev spaces
• The measure of the critical values of differentiable maps
• Function theory

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