(2005) Bettiol, Piernicola; Mathematics; Functional Analysis and Applications

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We prove an existence and uniqueness result for the solutions to the Skorokhod problem on uniformly prox-regular sets through a deterministic approach. This result can be applied in order to investigate some regularity properties of the value function for differential games reflection on the boundary.

(2007-02-02T09:06:13Z) Bettiol, Piernicola; Frankowska, Helene; Mathematics; Functional Analysis and Applications

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In this paper we consider a Bolza optimal control problem under state constraints and provide a sufficient condition for any Lipschitz trajectory satisfying the maximum principle to be a normal extremal. In the difference with the previous works we allow the initial condition to be fixed and consider less regular state constraints. To prove normality we use J.Yorke type linearization of control systems and show the existence of solution to a linearized control system satisfying new state constraints defined, in turn, by linearization of the original set of constraints along the extremal trajectory.

(2005) Bettiol, Piernicola; Frankowska, Helene; Mathematics; Functional Analysis and Applications

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Consider a differential inclusion under state constraints x'(t) F(t, x(t)), x(t) K, where F is a closed convex, not necessarily bounded set-valued map, which is measurable in t and k(t)-Lipschitz in x (with k(ยท) L1) and K Rn is a closed set with smooth boundary. ......