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(Almost) Everything you always wanted to know about deterministic control problems in stratified domains

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  • 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 $\mathbb{R}^N$. 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.
    Mathematics Subject Classification: Primary: 49L20, 49L25; Secondary: 35F21.


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