On the second boundary value problem for special Lagrangian curvature potential equation

TL;DR

This paper addresses the second boundary value problem for the special Lagrangian curvature potential equation, establishing existence and uniqueness of smooth convex solutions through a priori estimates and the method of continuity.

Contribution

It extends previous work by providing new existence and uniqueness results for the second boundary problem in this context.

Findings

Existence of smooth uniformly convex solutions

Uniqueness of solutions under given boundary conditions

Application of a priori estimates and continuity method

Abstract

This is a sequel to [1] and [2], which study the second boundary problem for special Lagrangian curvature potential equation. As consequences, we obtain the existence and uniqueness of the smooth uniformly convex solution by the method of continuity through carrying out a-priori estimate on the solutions.