A minimal time problem with linear dynamics and convex target is considered. It is shown, essentially, that the epigraph of the minimal time function $T(\cdot)$ is $\varphi$-convex (i.e., it satisfies a kind of exterior sphere condition with locally uniform radius), provided $T(\cdot)$ is continuous. Several regularity properties are derived from results in [G. Colombo and A. Marigonda, Calc. Var. Partial Differential Equations, 25 (2005), pp. 1-31], including twice a.e. differentiability of $T(\cdot)$ and local estimates on the total variation of $DT$.

Some new regularity properties for the minimal time function

MARIGONDA, ANTONIO;
2006-01-01

Abstract

A minimal time problem with linear dynamics and convex target is considered. It is shown, essentially, that the epigraph of the minimal time function $T(\cdot)$ is $\varphi$-convex (i.e., it satisfies a kind of exterior sphere condition with locally uniform radius), provided $T(\cdot)$ is continuous. Several regularity properties are derived from results in [G. Colombo and A. Marigonda, Calc. Var. Partial Differential Equations, 25 (2005), pp. 1-31], including twice a.e. differentiability of $T(\cdot)$ and local estimates on the total variation of $DT$.
2006
nonsmooth analysis; proximally smooth and $\varphi$-convex sets; small time controllability; functions with $\varphi$-convex epigraph
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/336563
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