Global $C^{1,\hat{I}\pm }$ regularity for Monge-Ampère equations on planar convex domains

Qing Han, Jiakun Liu, Yang Zhou

In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation $\det D^{2}u=f$ on strictly convex but not uni…