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semiconcavity.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Regularity along optimaltrajectories of the value function of a Mayer problem
Carlo Sinestrari
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 10 / Issue 4 / October 2004

Published online by Cambridge University Press:

15 October 2004, pp. 666-676

Print publication:

October 2004
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We consider an optimal control problem of Mayer type and prove that,under suitable conditions on the system, the value function isdifferentiable along optimal trajectories, except possibly at theendpoints. We provide counterexamples to show that this property may failto hold if some of our conditions are violated. We then apply our regularityresult to derive optimality conditions for the trajectories of the system.