We establish well-posedness of initial-boundary value problems for continuity
equations with BV (bounded total variation) coefficients. We do not prescribe
any condition on the orientation of the coefficients at the boundary of the
domain. We also discuss some examples showing that, regardless the orientation
of the coefficients at the boundary, uniqueness may be violated as soon as the
BV regularity deteriorates at the boundary.Comment: 25 pages, 5 figure
