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Semiconcavity for optimal control problems with exit time

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  • In this paper a semiconcavity result is obtained for the value function of an optimal exit time problem. The related state equation is of general form

    $\dot y(t)=f(y(t),u(t))$,  $y(t)\in\mathbb R^n$, $u(t)\in U\subset \mathbb R^m$.

    However, suitable assumptions are needed relating $f$ with the running and exit costs.
    The semiconcavity property is then applied to obtain necessary optimality conditions, through the formulation of a suitable version of the Maximum Principle, and to study the singular set of the value function.

    Mathematics Subject Classification: 49L20, 49K30.


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