@article{Noarov_2019, title={On the correct definition of the flow of a discontinuous solenoidal vector field}, volume={71}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/1505}, abstractNote={UDC 517.51 <br> We prove inequalities connecting a flow through the $(n- 1)$-dimensional surface $S$ of a smooth solenoidal vector field
with 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, more
precisely, of the class of vector fields that are equal almost everywhere with respect to the Lebesque measure).}, number={8}, journal={Ukrainsâ€™kyi Matematychnyi Zhurnal}, author={Noarov, A. I.}, year={2019}, month={Aug.}, pages={1141-1149} }