Global C^1, regularity for Monge-Ampère equations on planar convex domains

Key Points

• Global Hölder gradient estimates were established for solutions to the Monge-Ampère equation.
• The research involved Dirichlet problems defined on strictly convex but not uniformly convex domain.
• The Monge-Ampère equations serve as a vital tool in differential geometry and optimal transport theory.
• This finds relevance in understanding geometric properties of solutions in broader contexts, extending their use.