Regularity for the Monge-Ampère equation by doubling

2023/11/29 by Shankar, Ravi, Yuan, Yu · 2 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.17291

Abstract

We give a new proof for the interior regularity of strictly convex solutions of the Monge-Ampère equation. Our approach uses a doubling inequality for the Hessian in terms of the extrinsic distance function on the maximal Lagrangian submanifold determined by the potential equation.

Cited by

• Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints
• Pogorelov type interior C² estimate for Hessian quotient equation and its application

Related

• New Approach for Interior Regularity of Monge-Ampère Equations
• Partial regularity for singular solutions to the Monge-Ampere equation
• Sobolev regularity for Monge-Ampère type equations
• Global regularity for the Monge-Ampère equation with natural boundary condition
• Global C^1,α regularity for Monge-Ampère equations on planar convex domains