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Flows of measures generated by vector fields. / Paolini, Emanuele; Stepanov, Eugene.

In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Vol. 148, No. 4, 01.08.2018, p. 773-818.

Research output: Contribution to journal › Article › peer-review

Harvard

Paolini, E & Stepanov, E 2018, 'Flows of measures generated by vector fields', Proceedings of the Royal Society of Edinburgh Section A: Mathematics, vol. 148, no. 4, pp. 773-818. https://doi.org/10.1017/S0308210517000312

APA

Paolini, E., & Stepanov, E. (2018). Flows of measures generated by vector fields. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 148(4), 773-818. https://doi.org/10.1017/S0308210517000312

Vancouver

Paolini E, Stepanov E. Flows of measures generated by vector fields. Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2018 Aug 1;148(4):773-818. https://doi.org/10.1017/S0308210517000312

Author

Paolini, Emanuele ; Stepanov, Eugene. / Flows of measures generated by vector fields. In: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 2018 ; Vol. 148, No. 4. pp. 773-818.

BibTeX

@article{1f1fbc73eb5f4c378c80be23f85fd811,
title = "Flows of measures generated by vector fields",
abstract = "The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure 'flows along' the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.",
keywords = "continuity equation, flow of measures, integral curve, measurable vector field, metric current",
author = "Emanuele Paolini and Eugene Stepanov",
year = "2018",
month = aug,
day = "1",
doi = "10.1017/S0308210517000312",
language = "English",
volume = "148",
pages = "773--818",
journal = "Royal Society of Edinburgh - Proceedings A",
issn = "0308-2105",
publisher = "Cambridge University Press",
number = "4",

}

RIS

TY - JOUR

T1 - Flows of measures generated by vector fields

AU - Paolini, Emanuele

AU - Stepanov, Eugene

PY - 2018/8/1

Y1 - 2018/8/1

N2 - The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure 'flows along' the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.

AB - The scope of the paper is twofold. We show that for a large class of measurable vector fields in the sense of Weaver (i.e. derivations over the algebra of Lipschitz functions), called in the paper laminated, the notion of integral curves may be naturally defined and characterized (when appropriate) by an ordinary differential equation. We further show that for such vector fields the notion of a flow of the given positive Borel measure similar to the classical one generated by a smooth vector field (in a space with smooth structure) may be defined in a reasonable way, so that the measure 'flows along' the appropriately understood integral curves of the given vector field and the classical continuity equation is satisfied in the weak sense.

KW - continuity equation

KW - flow of measures

KW - integral curve

KW - measurable vector field

KW - metric current

UR - http://www.scopus.com/inward/record.url?scp=85051325517&partnerID=8YFLogxK

U2 - 10.1017/S0308210517000312

DO - 10.1017/S0308210517000312

M3 - Article

AN - SCOPUS:85051325517

VL - 148

SP - 773

EP - 818

JO - Royal Society of Edinburgh - Proceedings A

JF - Royal Society of Edinburgh - Proceedings A

SN - 0308-2105

IS - 4

ER -

ID: 36024030