Tangential Regularity in the Space of Directional-Morphological Transitions

The space of directional-morphological transitions is analyzed and a tangential regularity result is established for the subset $\mathcal{V}$. This subset arises in a natural way when one considers viability problems where both, trajectories and constraints, are evolving in time governed by differential and morphological equations, respectively. Furthermore a control problem associated with this kind of evolutionary-morphological systems is studied.