The union of uniform closed balls conjecture

Chadi Nour; Ronald Stern; Jean Takche

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Remark on a conjectured characterization of the sphere

Rolf Schneider (1975)

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"The Optiverse" and Other Sphere Eversions

John M. Sullivan (1999)

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Interior sphere property of attainable sets and time optimal control problems

Piermarco Cannarsa, Hélène Frankowska (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper studies the attainable set at time for the control system $\dot{y} (t) = f (y (t), u (t)) u (t) \in U$ showing that, under suitable assumptions on , such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C-regularity for boundaries of attainable sets.