C1 MEASURE RESPECTING MAPS PRESERVE BV IFF THEY HAVE BOUNDED DERIVATIVE

Ferruccio COLOMBINI; Tao LUO; Jeffrey RAUCH

doi:10.4310/MAA.2011.v18.n2.a2

C¹ MEASURE RESPECTING MAPS PRESERVE BV IFF THEY HAVE BOUNDED DERIVATIVE

Ferruccio COLOMBINI, Tao LUO, Jeffrey RAUCH

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

If Ω_j ∈ R^d (d ≥ 2) are bounded open subsets and Φ ∈ C¹ (Ω₁ ; Ω₂) respects Lebesgue measure and satisfies F ◦ Φ ∈ BV (Ω₁) for all F ∈ BV (Ω₂) then Φ is uniformly Lipschitzean.

Original language	English
Pages (from-to)	159–163
Journal	Methods and Applications of Analysis
Volume	18
Issue number	2
DOIs	https://doi.org/10.4310/MAA.2011.v18.n2.a2
Publication status	Published - Jun 2011
Externally published	Yes

Research Keywords

C1 measure respecting maps
BV regularity
Uniformly Lipschitzean

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Cite this

@article{27b0605f86014e6c933d8d885dd34953,

title = "C1 MEASURE RESPECTING MAPS PRESERVE BV IFF THEY HAVE BOUNDED DERIVATIVE",

abstract = "If Ωj ∈ Rd (d ≥ 2) are bounded open subsets and Φ ∈ C1 (Ω1 ; Ω2) respects Lebesgue measure and satisfies F ◦ Φ ∈ BV (Ω1) for all F ∈ BV (Ω2) then Φ is uniformly Lipschitzean.",

keywords = "C1 measure respecting maps, BV regularity, Uniformly Lipschitzean",

author = "Ferruccio COLOMBINI and Tao LUO and Jeffrey RAUCH",

year = "2011",

month = jun,

doi = "10.4310/MAA.2011.v18.n2.a2",

language = "English",

volume = "18",

pages = "159–163",

journal = "Methods and Applications of Analysis",

issn = "1073-2772",

publisher = "International Press of Boston",

number = "2",

}

TY - JOUR

T1 - C1 MEASURE RESPECTING MAPS PRESERVE BV IFF THEY HAVE BOUNDED DERIVATIVE

AU - COLOMBINI, Ferruccio

AU - LUO, Tao

AU - RAUCH, Jeffrey

PY - 2011/6

Y1 - 2011/6

N2 - If Ωj ∈ Rd (d ≥ 2) are bounded open subsets and Φ ∈ C1 (Ω1 ; Ω2) respects Lebesgue measure and satisfies F ◦ Φ ∈ BV (Ω1) for all F ∈ BV (Ω2) then Φ is uniformly Lipschitzean.

AB - If Ωj ∈ Rd (d ≥ 2) are bounded open subsets and Φ ∈ C1 (Ω1 ; Ω2) respects Lebesgue measure and satisfies F ◦ Φ ∈ BV (Ω1) for all F ∈ BV (Ω2) then Φ is uniformly Lipschitzean.

KW - C1 measure respecting maps

KW - BV regularity

KW - Uniformly Lipschitzean

U2 - 10.4310/MAA.2011.v18.n2.a2

DO - 10.4310/MAA.2011.v18.n2.a2

M3 - RGC 21 - Publication in refereed journal

SN - 1073-2772

VL - 18

SP - 159

EP - 163

JO - Methods and Applications of Analysis

JF - Methods and Applications of Analysis

IS - 2

ER -