I'm reading this paper relating to optimal investment with transaction costs where some value function $F(x)$ is optimized. At some boundary $x=u$ it will be optimal to pay a proportional cost $C$ which gives the boundary condition
\begin{equation} F'(u) = -C \end{equation}
The author argues that optimality also implies a boundary condition for the second derivative
\begin{equation} F''(u) = 0 \end{equation}
but I'm struggling to understand why this is the case. Any hints that will help me understand the intuition behind this condition?