# American Institute of Mathematical Sciences

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December  2004, 3(4): 757-774. doi: 10.3934/cpaa.2004.3.757

## Semiconcavity of the value function for exit time problems with nonsmooth target

 1 Dipartimento di Matematica, Università di Roma, Via della Ricerca Scientifica 1, 00133 Roma

Received  December 2003 Revised  May 2004 Published  September 2004

We prove semiconcavity of the value function of a nonlinear optimal control problem where the cost functional depends on the arrival time of the trajectory on a given target set. We make suitable smoothness assumptions on the dynamics of the system, while the target set can be completely general. As a corollary, we prove differentiability of the value function for a class of linear systems.
Citation: Carlo Sinestrari. Semiconcavity of the value function for exit time problems with nonsmooth target. Communications on Pure & Applied Analysis, 2004, 3 (4) : 757-774. doi: 10.3934/cpaa.2004.3.757
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