Generalized \(N\)-property and Sard theorem for Sobolev maps
type: Item
instance of: scholarly article
title: Generalized \(N\)-property and Sard theorem for Sobolev maps
zbMATH Open document ID: 1258.35056
DOI: 10.4171/RLM/641
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2013-01-21T00:00:00Z
review text: Summary: I report on some recent extensions of the Lusin \(N\)-property and the Sard theorem for Sobolev maps, which have been obtained in a joint work with \textit{M. Csörnyei} and \textit{B. Kirchheim} [``On the Sard theorem for Sobolev maps'' (in preparation)] and \textit{M. Csörnyei, E. D'Aniello} and \textit{B. Kirchheim} [``Generalized Lusin \(N\)-property for Sobolev maps'' (in preparation)]. Our research was originally motivated by questions related to the uniqueness of weak solutions for the continuity equation associated to a vector field with Sobolev regularity.
Mathematics Subject Classification ID: 35F10
Mathematics Subject Classification ID: 35L03
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 26B35
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 58K05
zbMATH DE Number: 6127545
zbMATH Keywords: Lusin N-property
zbMATH Keywords: flow associated to a vector field
zbMATH Keywords: continuity equation
author: Giovanni Alberti
MaRDI profile type: Publication
cites work: A uniqueness result for the continuity equation in two dimensions
cites work: Transport equation and Cauchy problem for BV vector fields
cites work: The Flow Associated to Weakly Differentiable Vector Fields: Recent Results and Open Problems
cites work: Toward a Precise Smoothness Hypothesis in Sard's Theorem
cites work: On the Morse-Sard property and level sets of Sobolev and BV functions
cites work: Q3598146
cites work: Morse-Sard theorem in Sobolev spaces
cites work: Q4831546
cites work: Ordinary differential equations, transport theory and Sobolev spaces
cites work: A simple proof of the Morse-Sard theorem in Sobolev spaces
cites work: Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems
cites work: Q4328334
cites work: The measure of the critical values of differentiable maps
cites work: A function not constant on a connected set of critical points
cites work: Weakly Differentiable Functions
description: scientific article; zbMATH DE number 6127545