TY - JOUR
AU - A. I. Noarov
PY - 2019/08/25
Y2 - 2022/10/01
TI - On the correct definition of the flow of a discontinuous solenoidal vector field
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 71
IS - 8
SE - Short communications
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1505
AB - UDC 517.51 We prove inequalities connecting a flow through the $(n- 1)$-dimensional surface $S$ of a smooth solenoidal vector fieldwith its $L^{p}(U)$-norm ($U$ is an $n$-dimensional domain that contains $S$). On the basis of these inequalities, we propose a correct definition of the flow through the surface $S$ of a discontinuous solenoidal vector field $f \in L^{p}(U)$ (or, moreprecisely, of the class of vector fields that are equal almost everywhere with respect to the Lebesque measure).
ER -