  We revisit the pioneering work of Bressan \& Hong on deterministic control
problems in stratified domains, i.e. control problems for which the dynamic and
the cost may have discontinuities on submanifolds of R N . By using slightly
different methods, involving more partial differential equations arguments, we
(i) slightly improve the assumptions on the dynamic and the cost; (ii) obtain a
comparison result for general semi-continuous sub and supersolutions (without
any continuity assumptions on the value function nor on the
sub/supersolutions); (iii) provide a general framework in which a stability
result holds.
