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Discontinuous solutions of Hamilton-Jacobi-Bellman equation under state constraints

Hélène Frankowska 1 Marco Mazzola 1
1 C&O - Equipe combinatoire et optimisation
IMJ-PRG - Institut de Mathématiques de Jussieu - Paris Rive Gauche
Abstract : This article is devoted to the Hamilton-Jacobi partial differential equation tV=Htx−xV V(1x)=g(x) on on [01] where the Hamiltonian H:[01]RnRnR is convex and positively homogeneous with respect to the last variable, Rn is open and g:RnR+ is lower semicontinuous. Such Hamiltonians do arise in the optimal control theory. We apply the method of generalized characteristics to show uniqueness of lower semicontinuous solution of this first order PDE. The novelty of our setting lies in the fact that we do not ask regularity of the boundary of Ω and extend the Soner inward pointing condition in a nontraditional way to get uniqueness in the class of lower semicontinuous functions.
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https://hal.inria.fr/hal-00710717
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Submitted on : Thursday, June 21, 2012 - 3:17:47 PM
Last modification on : Tuesday, December 15, 2020 - 4:00:50 AM

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Hélène Frankowska, Marco Mazzola. Discontinuous solutions of Hamilton-Jacobi-Bellman equation under state constraints. Calculus of Variations and Partial Differential Equations, Springer Verlag, 2013, 46, pp.725-747. ⟨10.1007/s00526-012-0501-8⟩. ⟨hal-00710717⟩

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