Explicit gradient estimates for minimal Lagrangian surfaces of dimension two

TL;DR

This paper provides explicit, uniform interior estimates for the Hessian and gradient of solutions to special Lagrangian equations in two dimensions, aiding the understanding of minimal Lagrangian surfaces.

Contribution

It introduces explicit a priori interior estimates for minimal Lagrangian surfaces of dimension two, applicable to all phases, which was previously unavailable.

Findings

Derived explicit interior Hessian estimates

Established uniform gradient bounds

Applicable to all phases of special Lagrangian equations

Abstract

We derive explicit, uniform, a priori interior Hessian and gradient estimates for special Lagrangian equations of all phases in dimension two.