Luzin's condition (N) and Sobolev mappings
type: Item
instance of: scholarly article
title: Luzin's condition (N) and Sobolev mappings
zbMATH Open document ID: 1257.26010
DOI: 10.4171/RLM/639
author: Pekka Koskela
author: Jan Malý
author: Thomas Zürcher
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: For the purpose of change of variables in integral, it is important to know how to verify Luzin's condition (N) for Sobolev mappings. We survey some results on this topic sorted according to the method. We discuss the method of absolute continuity, results obtained via degree, and results based on the interplay between integrability and modulus of continuity.
Mathematics Subject Classification ID: 26B15
Mathematics Subject Classification ID: 28A75
Mathematics Subject Classification ID: 30C65
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 51M25
zbMATH DE Number: 6127543
zbMATH Keywords: Luzin's condition (N)
zbMATH Keywords: change of variables in integral
zbMATH Keywords: area formula
zbMATH Keywords: Sobolev mappings
Wikidata QID: Q110125040
MaRDI profile type: Publication
cites work: A geometrical approach to monotone functions in \(\mathbb{R}^n\)
cites work: The Jacobian determinant revisited
cites work: Sulle trasformazioni continue
cites work: Some remarks on the distributional Jacobian
cites work: Q3134551
cites work: Surface area. I
cites work: Q4838489
cites work: Estimates of Jacobians by subdeterminants.
cites work: Area and the area formula
cites work: A remark on the equality \(\text{det} Df=\text{Det} Df\)
cites work: Q4235447
cites work: Limits of the improved integrability of the volume forms
cites work: Change of variables formula under minimal assumptions
cites work: Q4328577
cites work: Sobolev Peano cubes
cites work: Some properties of the degree for a class of Sobolev maps
cites work: Q4548127
cites work: On the integrability of the Jacobian under minimal hypotheses
cites work: Functions of bounded higher variation
cites work: Density properties of harmonic measure
cites work: Q4429898
cites work: On functions with derivatives in a Lorentz space
cites work: Mappings of finite distortion: sharp Orlicz-conditions
cites work: Minimal assumptions for the integrability of the Jacobian
cites work: Absolutely continuous functions of several variables
cites work: Transformations by functions in Sobolev spaces and lower semicontinuity for parametric variational problems
cites work: Lusin's condition (N) and mappings with nonnegative Jacobians
cites work: On a new class of elastic deformations not allowing for cavitation
cites work: An existence theory for nonlinear elasticity that allows for cavitation
cites work: Q3227685
cites work: Q3772469
cites work: Q3992482
cites work: Area, coarea, and approximation in \(W^{1,1}\)
cites work: Q3828253
cites work: Topological and geometrical properties of mappings with summable Jacobian in Sobolev classes. I
cites work: Peano cubes with derivatives in a Lorentz space
description: scientific article; zbMATH DE number 6127543