On the exceptional sets of the flux of a bounded vectorfield, J. Math. Pures Appl., 82(9), 2003. 1191-1217.
For each purely n-1 unrectifiable compact set C ⊂ Rn such that 0 < Hn-1(C) < ∞, there is a bounded Borel measurable vectorfield v : Rn → Rn whose flux vanishes in Rn ∼ C but not in Rn.