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. 102-11610.1051/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 = , with a running cost . We prove an interior sphere property for the level sets of the corresponding value function . From such a property we obtain a semiconcavity result for , as well as perimeter estimates for the attainable sets of a symmetric control system.