# 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

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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

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