Hessian Estimates for Lagrangian mean curvature equation

TL;DR

This paper establishes interior Hessian estimates for solutions to the Lagrangian mean curvature equation under supercritical phase conditions, advancing understanding of geometric PDEs in symplectic geometry.

Contribution

It provides new a priori Hessian bounds for the Lagrangian mean curvature equation with supercritical phase, a key step in geometric analysis.

Findings

Derived interior Hessian estimates for supercritical phase cases

Bounded second derivatives imply regularity of solutions

Enhances understanding of Lagrangian mean curvature equations

Abstract

In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.