Asymptotic expansion at infinity of solutions of Monge-Amp\`ere type equations

TL;DR

This paper derives a detailed asymptotic expansion at infinity for solutions to Monge-Ampère type equations, originating from mean curvature equations of Lagrangian graphs, refining previous zero mean curvature and Monge-Ampère studies.

Contribution

It provides a quantitative asymptotic expansion at infinity for solutions of Monge-Ampère type equations, enhancing understanding of their behavior at large scales.

Findings

Derived explicit asymptotic expansion at infinity

Refined previous results on zero mean curvature equations

Extended analysis to Monge-Ampère type equations

Abstract

We obtain a quantitative expansion at infinity of solutions for a kind of Monge-Amp\`ere type equations that origin from mean curvature equations of Lagrangian graph $(x,Du(x))$ and refine the previous study on zero mean curvature equations and the Monge-Amp\`ere equations.