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.
Abstract
Abstract In this paper, we establish the global Hölder gradient estimate for solutions to the Dirichlet problem of the Monge-Ampère equation D²u = f on strictly convex but not uniformly convex domain.