The Dirichlet problem of generalized special Lagrangian type equations and curvature version

Abstract This article focuses on two kinds of generalized special Lagrangian type equations. We investigate the Dirichlet problem for these equations with supercritical phase and critical phase in $\mathbb {R}^n$ , deriving the a priori estimates and establishing the existence under the assumption of a subsolution. Furthermore, we also consider the corresponding special Lagrangian curvature type equations with supercritical phase and critical phase.