  In this note we revisit previous Pogorelov type interior and global second
derivative estimates of the author, F. Jiang and J. Liu for solutions of
Monge-Amp`ere type partial differential equations. Taking account of recent
strict convexity regularity results of Guillen, Kitagawa and Rankin, and
following our earlier work in the optimal transportation case, we remove the
monotonicity assumptions in the more general case of generated Jacobian
equations and consequently in the subsequent application to classical
solvability and global regularity for second boundary value problems.
