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Interior sphere property for level sets of thevalue function of an exit time problem

Published online by Cambridge University Press:  23 January 2009

Marco Castelpietra*
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy. castelpi@mat.uniroma2.it
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Abstract

We consider an optimal control problem for a system of the form $\dot{x}$ = 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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2008

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References

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Sinestrari, C., Semiconcavity of the value function for exit time problems with nonsmooth target. Commun. Pure Appl. Anal. 3 (2004) 757774. CrossRef

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