  We continue our study of the Cauchy problem for the homogeneous (real and
complex) Monge-Ampere equation (HRMA/HCMA). In the prequel a quantum mechanical
approach for solving the HCMA was developed, and was shown to coincide with the
well-known Legendre transform approach in the case of the HRMA. In this
article---that uses tools of convex analysis and can be read independently---we
prove that the candidate solution produced by these methods ceases to solve the
HRMA, even in a weak sense, as soon as it ceases to be differentiable.
