SOME NEW REGULARITY PROPERTIES FOR THE MINIMAL TIME FUNCTION.

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(·) is ϕ-convex (i.e., it satisfies a kind of exterior sphere condition with locally uniform radius), provided T(·) 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(·) and local estimates on the total variation of DT. [ABSTRACT FROM AUTHOR]