Quantitative differentiation

A general formulation

Research output: Contribution to journalArticle

Abstract

Let dx denote Lebesgue measure on ℝ n. With respect to the measure C = r -1 dr × dx on the collection of balls B r(x) ⊂ ℝ n, the subcollection of balls B r(x) ⊂ B 1(0) has infinite measure. Let f: B 1(0) → ℝ have bounded gradient, |∇f

Original languageEnglish (US)
Pages (from-to)1641-1670
Number of pages30
JournalCommunications on Pure and Applied Mathematics
Volume65
Issue number12
DOIs
StatePublished - Dec 2012

Fingerprint

Ball
Formulation
Lebesgue Measure
Gradient
Denote

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Quantitative differentiation : A general formulation. / Cheeger, Jeff.

In: Communications on Pure and Applied Mathematics, Vol. 65, No. 12, 12.2012, p. 1641-1670.

Research output: Contribution to journalArticle

@article{83cc1d7216a441ddb7b69d845b80359d,
title = "Quantitative differentiation: A general formulation",
abstract = "Let dx denote Lebesgue measure on ℝ n. With respect to the measure C = r -1 dr × dx on the collection of balls B r(x) ⊂ ℝ n, the subcollection of balls B r(x) ⊂ B 1(0) has infinite measure. Let f: B 1(0) → ℝ have bounded gradient, |∇f",
author = "Jeff Cheeger",
year = "2012",
month = "12",
doi = "10.1002/cpa.21424",
language = "English (US)",
volume = "65",
pages = "1641--1670",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "Wiley-Liss Inc.",
number = "12",

}

TY - JOUR

T1 - Quantitative differentiation

T2 - A general formulation

AU - Cheeger, Jeff

PY - 2012/12

Y1 - 2012/12

N2 - Let dx denote Lebesgue measure on ℝ n. With respect to the measure C = r -1 dr × dx on the collection of balls B r(x) ⊂ ℝ n, the subcollection of balls B r(x) ⊂ B 1(0) has infinite measure. Let f: B 1(0) → ℝ have bounded gradient, |∇f

AB - Let dx denote Lebesgue measure on ℝ n. With respect to the measure C = r -1 dr × dx on the collection of balls B r(x) ⊂ ℝ n, the subcollection of balls B r(x) ⊂ B 1(0) has infinite measure. Let f: B 1(0) → ℝ have bounded gradient, |∇f

UR - http://www.scopus.com/inward/record.url?scp=84867615099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867615099&partnerID=8YFLogxK

U2 - 10.1002/cpa.21424

DO - 10.1002/cpa.21424

M3 - Article

VL - 65

SP - 1641

EP - 1670

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 12

ER -