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Hölder estimates for trajectories of differential inclusions and HJB equations with state constraints

Giancarlo Facchi 1 Daniel Hoehener 2
2 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
Abstract : We consider the differential inclusion x˙∈F(t,x) , with F measurable in t and Lipschitz in x, together with the state constraint x(t)∈Ω and prove the existence of neighboring trajectories lying in the interior of Ω. Using this result, we can characterize the Value Function of the Bolza Problem as the unique lower semicontinuous solution to the corresponding Hamilton-Jacobi-Bellman equation.
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https://hal.inria.fr/hal-00800194
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Submitted on : Wednesday, March 13, 2013 - 12:56:28 PM
Last modification on : Thursday, December 10, 2020 - 12:34:41 PM

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Giancarlo Facchi, Daniel Hoehener. Hölder estimates for trajectories of differential inclusions and HJB equations with state constraints. Nonlinear Differential Equations and Applications, Springer Verlag, 2013, 20 (3), pp.1079-1104. ⟨10.1007/s00030-012-0198-6⟩. ⟨hal-00800194⟩

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