Hessian and gradient estimates for three dimensional special Lagrangian Equations with large phase

TL;DR

This paper establishes interior Hessian and gradient estimates for three-dimensional special Lagrangian equations with large phase, advancing understanding of their regularity properties.

Contribution

It provides the first a priori interior estimates for these equations when the phase exceeds a critical value in three dimensions.

Findings

Hessian estimates derived for large phase

Gradient estimates established in the same setting

Advances regularity theory for special Lagrangian equations

Abstract

We derive a priori interior Hessian and gradient estimates for special Lagrangian equation of phase at least a critical value in dimension three.