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Stable representation of convex Hamiltonians

Abstract : Existence and uniqueness of solutions to a Hamilton-Jacobi equation with the Hamiltonian H convex with respect to the last variable can be proved by associating to H either a Calculus of Variations or an optimal control problem. The data of the new problem should be so that its Hamiltonian coincides with H and should also inherit appropriate continuity/local Lipschitz continuity properties of H. In other words, H can be represented by functions describing an optimization problem. In this paper we provide further developments of representation theorems from Rampazzo (2005). In particular, our results imply continuous dependence of representations on the mapping H. We apply them to study existence of solutions to the Hamilton-Jacobi equation with H possibly discontinuous in t.
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Submitted on : Thursday, January 30, 2014 - 7:42:46 PM
Last modification on : Sunday, June 26, 2022 - 5:26:29 AM



Hélène Frankowska, Hayk Sedrakyan. Stable representation of convex Hamiltonians. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2014, 100, pp.30-42. ⟨10.1016/⟩. ⟨hal-00939497⟩



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