Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Flows of measures generated by vector fields. / Paolini, Emanuele; Stepanov, Eugene.
в: Proceedings of the Royal Society of Edinburgh Section A: Mathematics, Том 148, № 4, 01.08.2018, стр. 773-818.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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