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A boundary value problem for the minimum-time function. (English) Zbl 0682.49034

Summary: A natural boundary value problem for the dynamic programming partial differential equation associated with the minimum time problem is proposed. The minimum time function is shown to be the unique viscosity solution of this boundary value problem.

MSC:

49L20 Dynamic programming in optimal control and differential games
35F30 Boundary value problems for nonlinear first-order PDEs
49K15 Optimality conditions for problems involving ordinary differential equations
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