Generalized \(N\)-property and Sard theorem for Sobolev maps

DOI10.4171/RLM/641zbMath1258.35056MaRDI QIDQ1932681

Giovanni Alberti

Publication date: 21 January 2013

Published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni (Search for Journal in Brave)

zbMATH Keywords

continuity equationLusin N-propertyflow associated to a vector field

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Length, area, volume, other geometric measure theory (28A75) Special properties of functions of several variables, Hölder conditions, etc. (26B35) Initial value problems for linear first-order PDEs (35F10) Critical points of functions and mappings on manifolds (58K05) Initial value problems for first-order hyperbolic equations (35L03)

Related Items (10)

A bridge between Dubovitskiĭ-Federer theorems and the coarea formula ⋮ Scaled oscillation and level sets ⋮ The generalized Morse-Sard theorem ⋮ On some universal Morse-Sard type theorems ⋮ Almost Everywhere Nonuniqueness of Integral Curves for Divergence-Free Sobolev Vector Fields ⋮ Hausdorff measure of critical set for Luzin \(N\) condition ⋮ On the Luzin \(N\)-property and the uncertainty principle for Sobolev mappings ⋮ Nonsmooth Morse-Sard theorems ⋮ Positive solutions of transport equations and classical nonuniqueness of characteristic curves ⋮ The Morse-Sard theorem and Luzin \(N\)-property: a new synthesis for smooth and Sobolev mappings

Cites Work

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• Weakly Differentiable Functions
• Toward a Precise Smoothness Hypothesis in Sard's Theorem
• Morse-Sard theorem in Sobolev spaces
• Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems
• The measure of the critical values of differentiable maps

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