Flows of measures generated by vector fields

Emanuele Paolini, Eugene Stepanov

Результат исследований: Научные публикации в периодических изданияхстатья


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.

Язык оригиналаанглийский
Страницы (с-по)773-818
Число страниц46
ЖурналProceedings of the Royal Society of Edinburgh Section A: Mathematics
Номер выпуска4
СостояниеОпубликовано - 1 авг 2018


Предметные области Scopus

  • Математика (все)