Boundary regularity for solutions to the linearized Monge-Ampère equations

Abstract

We obtain boundary Holder gradient estimates and regularity for solutions to the linearized Monge-Ampere equations under natural assumptions on the domain, Monge-Ampere measures and boundary data. Our results are affine invariant analogues of the boundary Holder gradient estimates of Krylov.

References in corpus (4)

• Interior estimates for solutions of Abreu's equation
• A localization property at the boundary for the Monge-Ampere equation
• Global $W^{2,p}$ estimates for the Monge-Ampere equation
• Some minimization problems in the class of convex functions with prescribed determinant

Cited by in corpus (3)

• Inhomogeneous Hopf-Oleĭnik Lemma and Applications. Part IV: Sharp Krylov Boundary Gradient Type Estimates for Solutions to Fully Nonlinear Differential Inequalities with unbounded coefficients and $C^{1,Dini}$ boundary data
• Monge Ampère functionals and the second boundary value problem
• On boundary Hölder gradient estimates for solutions to the linearized Monge-Ampère equations