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. castelpi@mat.uniroma2.it

Received: 25 November 2006
Revised: 18 September 2007

Abstract

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.