On the second boundary value problem for a class of fully nonlinear flows II

TL;DR

This paper extends previous work on fully nonlinear flows, establishing long-term existence and convergence for special Lagrangian equations with second boundary conditions, enabling prescribed boundary value problems.

Contribution

It advances the understanding of fully nonlinear parabolic flows by proving long-time existence and convergence for a broader class of special Lagrangian boundary value problems.

Findings

Established long-time existence of solutions.

Proved convergence of the flow.

Enabled prescribing second boundary conditions.

Abstract

This article is a continuation of earlier work [R.L. Huang and Y.H. Ye, On the second boundary value problem for a class of fully nonlinear flows I, to appear in International Mathematics Research Notices], where the long time existence and convergence were given on some general parabolic type special Lagrangian equations. The long time existence and convergence of the flow had been obtained in all cases. In particular, we can prescribe the second boundary value problems for a family of special Lagrangian graphs.