# Interior sphere property for level sets of the value function of an exit time problem

ESAIM: Control, Optimisation and Calculus of Variations (2009)

- Volume: 15, Issue: 1, page 102-116
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topCastelpietra, Marco. "Interior sphere property for level sets of the value function of an exit time problem." ESAIM: Control, Optimisation and Calculus of Variations 15.1 (2009): 102-116. <http://eudml.org/doc/250575>.

@article{Castelpietra2009,

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.
},

author = {Castelpietra, Marco},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Control theory; interior sphere property; value
function; semiconcavity; perimeter; control theory; value function},

language = {eng},

month = {1},

number = {1},

pages = {102-116},

publisher = {EDP Sciences},

title = {Interior sphere property for level sets of the value function of an exit time problem},

url = {http://eudml.org/doc/250575},

volume = {15},

year = {2009},

}

TY - JOUR

AU - Castelpietra, Marco

TI - Interior sphere property for level sets of the value function of an exit time problem

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2009/1//

PB - EDP Sciences

VL - 15

IS - 1

SP - 102

EP - 116

AB -
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.

LA - eng

KW - Control theory; interior sphere property; value
function; semiconcavity; perimeter; control theory; value function

UR - http://eudml.org/doc/250575

ER -

## References

top- O. Alvarez, P. Cardaliaguet and R. Monneau, Existence and uniqueness for dislocation dynamics with nonnegative velocity. Interfaces Free Bound.7 (2005) 415–434.
- P. Cannarsa and P. Cardaliaguet, Perimeter estimates for the reachable set of control problems. J. Convex Anal.13 (2006) 253–267.
- P. Cannarsa and H. Frankowska, Interior sphere property of attainable sets and time optimal control problems. ESAIM: COCV12 (2006) 350–370.
- P. Cannarsa and C. Sinestrari, Convexity properties of the minimun time function. Calc. Var. Partial Differential Equations3 (1995) 273–298.
- P. Cannarsa and C. Sinestrari, Semiconcave Functions, Hamilton-Jacobi Equations and Optimal Control. Birkhauser, Boston (2004).
- P. Cannarsa, C. Pignotti and C. Sinestrari, Semiconcavity for optimal control problems with exit time. Discrete Contin. Dynam. Systems6 (2000) 975–997.
- L.C. Evans and F. Gariepy, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics. Boca Raton (1992).
- C. Sinestrari, Semiconcavity of the value function for exit time problems with nonsmooth target. Commun. Pure Appl. Anal.3 (2004) 757–774.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.