Asymptotic expansion at infinity of solutions of special Lagrangian equations

TL;DR

This paper develops a high-order asymptotic expansion at infinity for solutions of certain fully nonlinear elliptic equations, including the Monge-Ampère and special Lagrangian equations, clarifying their behavior on exterior domains.

Contribution

It provides a precise asymptotic expansion at infinity for solutions of these equations, refining understanding of their behavior compared to entire solutions.

Findings

High-order asymptotic expansion at infinity for solutions

Refined understanding of the gap between exterior and entire solutions

Application to Monge-Ampère and special Lagrangian equations

Abstract

We obtain a quantitative high order expansion at infinity of solutions for a family of fully nonlinear elliptic equations on exterior domain, refine the study of the asymptotic behavior of the Monge-Amp\`ere equation, the special Lagrangian equation and other elliptic equations, and give the precise gap between exterior maximal (or minimal) gradient graph and the entire case.