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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
Marco Castelpietra*
Affiliation:
Dipartimento di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy. [email protected]
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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 interiorsphere property for the level sets of the corresponding valuefunction V. From such a property we obtain a semiconcavityresult for V, as well as perimeter estimates for the attainablesets of a symmetric control system.

Keywords

Control theoryinterior sphere propertyvaluefunctionsemiconcavityperimeter
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 1 , January 2009 , pp. 102 - 116
Copyright
© EDP Sciences, SMAI, 2008

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