Interior sphere property for level sets of the value function of an exit time problem
ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 1 , p. 102-116
doi : 10.1051/cocv:2008018
URL stable : http://www.numdam.org/item?id=COCV_2009__15_1_102_0

Classification:  93B03,  49L20,  49L25
We consider an optimal control problem for a system of the form $\stackrel{˙}{x}$ = $f\left(x,u\right)$, 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.

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