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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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