On the Dirichlet problem for special Lagrangian curvature potential equation

TL;DR

This paper establishes the existence of smooth solutions for a class of special Lagrangian curvature potential equations' Dirichlet problem, using a priori estimates and subsolution assumptions.

Contribution

It provides new existence results for smooth solutions to special Lagrangian curvature potential equations under specific boundary conditions.

Findings

Existence of smooth solutions proven.

A priori estimates for solutions established.

Results depend on the existence of a subsolution.

Abstract

In this paper, we study a class of special Lagrangian curvature potential equations and obtain the existence of smooth solutions for Dirichlet problem. The existence result is based on a priori estimates of global $C^{0}$, $C^{1}$ and $C^{2}$ norms of solutions under the assumption of existence of a subsolution.