On the solvability of Monge-Ampère type equations in non-uniformly convex domains (Q1191414)

The author studies the Dirichlet problem for Monge-Ampère equations (*) \(\text{det} D^ 2u=g(x,u,Du)\) in \(\Omega, \quad u=f\) on \(\partial\Omega\), in bounded convex domains \(\Omega\) in \(\mathbb{R}^ n\) which are not uniformly convex. He formulates precise necessary and sufficient conditions on \(g\) and \(f\) which guarantee the existence of a globally Lipschitz convex solution of (*). These reduce to those of \textit{N. S. Trudinger} and \textit{J.Urbas} [Bull. Austral. Math. Soc. 28, 217-231 (1983; Zbl 0524.35047)] in the case that \(\Omega\) is uniformly convex.