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We revisit the pioneering work of Bressan \& Hong on deterministic controlproblems in stratified domains, i.e. control problems for which the dynamic andthe cost may have discontinuities on submanifolds of R N . By using slightlydifferent methods, involving more partial differential equations arguments, we(i) slightly improve the assumptions on the dynamic and the cost; (ii) obtain acomparison result for general semi-continuous sub and supersolutions (withoutany continuity assumptions on the value function nor on thesub/supersolutions); (iii) provide a general framework in which a stabilityresult holds.

(Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains