Distributional divergence
= Distributional divergence
{title2=$\langle\operatorname{div}z,\eta\rangle=-\int z\cdot\nabla\eta$}
For a locally integrable <vector field>, this formula defines its divergence as a <distribution>. For a piecewise <smooth> field, a jump of its normal component across an interface adds a surface measure to the <smooth> divergences. A <continuous> normal component eliminates that measure, as follows by <integration by parts> on the two sides.