Uniqueness of viscosity solutions of a geometric fully nonlinear parabolic equation

TL;DR

This paper demonstrates that the comparison principle for viscosity solutions applies to a geometric fully nonlinear parabolic equation related to Lagrangian mean curvature flow, establishing uniqueness of solutions.

Contribution

It extends the comparison result to a new class of geometric fully nonlinear parabolic equations derived from Lagrangian mean curvature flow.

Findings

Comparison principle applies to the geometric equation

Uniqueness of viscosity solutions established

Applicable to equations from Lagrangian mean curvature flow

Abstract

We observe that the comparison result of Barles-Biton-Ley for viscosity solutions of a class of nonlinear parabolic equations can be applied to a geometric fully nonlinear parabolic equation which arises from the graphic solutions for the Lagrangian mean curvature flow.