Interior sphere property for level sets of the value function of an exit time problem
Marco Castelpietra (2009)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
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.