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arXiv · 1412.7556

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

G. Barles·Emmanuel Chasseigne
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Abstract

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.

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G. Barles, Emmanuel Chasseigne. 2014-12-23. (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains. https://arxiv.org/abs/1412.7556

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