Symmetry of solutions of minimal gradient graph equations on punctured space

Abstract

In this paper, we study symmetry and existence of solutions of minimal gradient graph equations on punctured space ${\mathbb{R}}^n\setminus \{0\}$, which include the Monge-Ampère equation, inverse harmonic Hessian equation and the special Lagrangian equation. This extends the classification results of Monge-Ampère equations. Under some conditions, we also give the characterization of the solvability on exterior Dirichlet problem in terms of their asymptotic behaviors.

References in corpus (3)

• Regularity for convex viscosity solutions of special Lagrangian equation
• A Remark on Monge-Ampère equation over exterior domains
• Global Monge-Ampere equation with asymptotically periodic data

Cited by in corpus (1)

• Asymptotic expansion and optimal symmetry of minimal gradient graph equations in dimension 2