Geodesic
Generalized Conjugacy in Hamilton-Jacobi Theory for Fully Convex Langrangians
Journal of convex analysis, Tome 9 (2002) no. 2, pp. 463-473.

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Control problems with fully convex Lagrangians and convex initial costs are considered. Generalized conjugacy and envelope representation in terms of a dualizing kernel are employed to recover the initial cost from the value function at some fixed future time, leading to a generalization of the cancellation rule for inf-convolution. Such recovery is possible subject to persistence of trajectories of a generalized Hamiltonian system, associated with the Lagrangian. Global analysis of Hamiltonian trajectories is carried out, leading to conditions on the Hamiltonian, and the corresponding Lagrangian, guaranteeing persistence of the trajectories.
Classification : 49L20, 93C10, 49N15
Mots-clés : Convex value functions, inf-convolution, Hopf-Lax formula, nonsmooth Hamiltonian dynamics, generalized conjugacy, fully convex Langrangians, optimal control 
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     author = {R. Goebel and R. T. Rockafellar},
     title = {Generalized {Conjugacy} in {Hamilton-Jacobi} {Theory} for {Fully} {Convex} {Langrangians}},
     journal = {Journal of convex analysis},
     pages = {463--473},
     publisher = {mathdoc},
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     year = {2002},
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R. Goebel; R. T. Rockafellar. Generalized Conjugacy in Hamilton-Jacobi Theory for Fully Convex Langrangians. Journal of convex analysis, Tome 9 (2002) no. 2, pp. 463-473. http://geodesic.mathdoc.fr/item/JCA_2002_9_2_JCA_2002_9_2_a8/