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

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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https://hal.archives-ouvertes.fr/hal-01097167
Contributor : Guy Barles Connect in order to contact the contributor
Submitted on : Monday, August 17, 2015 - 10:27:23 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM
Long-term archiving on: : Wednesday, November 18, 2015 - 10:38:23 AM

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  • HAL Id : hal-01097167, version 3
  • ARXIV : 1412.7556

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G Barles, Emmanuel Chasseigne. (Almost) Everything You Always Wanted to Know About Deterministic Control Problems in Stratified Domains. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2015, 10 (4), pp.809-836. ⟨hal-01097167v3⟩

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