Regularity for convex viscosity solutions of Lagrangian mean curvature equation

TL;DR

This paper proves that convex viscosity solutions to the Lagrangian mean curvature equation are regular when the Lagrangian phase function has H"older continuous second derivatives, advancing understanding of solution regularity under certain smoothness conditions.

Contribution

It establishes regularity results for convex viscosity solutions of the Lagrangian mean curvature equation under H"older continuity assumptions on the phase's second derivatives.

Findings

Convex viscosity solutions are regular with H"older continuous phase derivatives.

Provides conditions under which solutions to the Lagrangian mean curvature equation are smooth.

Enhances theoretical understanding of geometric PDEs in symplectic geometry.

Abstract

We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has H\"older continuous second derivatives.