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Partial and full sensitivity relations are obtained for nonautonomous optimal control problems with infinite horizon subject to state constraints, assuming the associated value function to be locally Lipschitz in the state. Sufficient structural conditions are given to ensure such a Lipschitz regularity in presence of a positive discount factor, as it is typical of macroeconomics models.

In this paper we investigate the existence and uniqueness of weak solutions of the nonautonomous Hamilton-Jacobi-Bellman equation on the domain (0, ∞) × Ω. The Hamiltonian is assumed to be merely measurable in time variable and the open set Ω may be unbounded with nonsmooth boundary. The set Ω is called here a state constraint. When state constraints arise, then classical analysis of Hamilton-Jacobi-Bellman equation lacks appropriate notion of solution because continuous solutions could not exist. In this work we propose a notion of weak solution for which, under a suitable controllability assumption, existence and uniqueness theorems are valid in the class of lower semicontinuous functions vanishing at infinity.

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