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Interior sphere property for level sets of the value function of an exit time problem. (English) Zbl 1155.49024
Summary: We consider an optimal control problem for a system of the form \(\dot{x} = f(x,u)\), with a running cost \(L\). We prove an interior sphere property for the level sets of the corresponding value function \(V\). From such a property we obtain a semiconcavity result for \(V\), as well as perimeter estimates for the attainable sets of a symmetric control system.

MSC:
49N60 Regularity of solutions in optimal control
93B03 Attainable sets, reachability
49L20 Dynamic programming in optimal control and differential games
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
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