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Optimal control with state-space constraint. I. (English) Zbl 0597.49023
The problem studied is the Hamilton-Jacobi-Bellman (HJB) equation associated to a deterministic optimal control problem with state space constraints. The principal results obtained are the following: 1) The optimal value function is the unique function that is a viscosity subsolution in the open domain, and a viscosity supersolution in the closed domain. 2) The optimal value function is bounded and uniformly continuous in the closed domain.
Reviewer: R.Gonzalez

MSC:
49L20 Dynamic programming in optimal control and differential games
35D99 Generalized solutions to partial differential equations
35J65 Nonlinear boundary value problems for linear elliptic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
60J60 Diffusion processes
93E20 Optimal stochastic control
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