Interior sphere property for level sets of the value function of an exit time problem
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della
Ricerca Scientifica 1, 00133 Roma, Italy. firstname.lastname@example.org
Revised: 18 September 2007
We consider an optimal control problem for a system of the form = f(x,u), 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.
Mathematics Subject Classification: 93B03 / 49L20 / 49L25
Key words: Control theory / interior sphere property / value function / semiconcavity / perimeter
© EDP Sciences, SMAI, 2008