Affiliations: [a] Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350), Fédération Denis Poisson (FR CNRS 2964), Université François Rabelais, Tours, France. E-mails: [email protected], [email protected], [email protected] | [b] IRMAR, UMR 6625, Université de Rennes 1, Rennes, France. E-mail: [email protected]
Correspondence:
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Corresponding author: Ariela Briani, Laboratoire de Mathématiques et Physique Théorique (UMR CNRS 7350), Fédération Denis Poisson (FR CNRS 2964), Université François Rabelais, Parc de Grandmont, 37200 Tours, France. E-mail: [email protected].
Abstract: We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space RN. For such optimal control problems, the three first authors have shown that several value functions can be defined, depending, in particular, if the choice is to use only “regular strategies” or to use also “singular strategies”. We study the homogenization problem in these two different cases. It is worth pointing out that, if the second one can be handled by usual partial differential equations method “à la Lions–Papanicolaou–Varadhan” with suitable adaptations, the first case has to be treated by control methods (dynamic programming).
