Abstract:We establish a Liouville type theorem for fully nonlinear uniformly elliptic equations in exterior domains in half spaces under quadratic boundary data and a quadratic growth condition, that is, any viscosity solution tends to a quadratic polynomial plus lower order terms at infinity with the rate at least $|x|^{-\alpha-n}$ for any $\alpha\in(0,1)$. As applications, this result can lead to Liouville type theorems for Monge-Amp`ere equations, k-Hessian equations and special Lagrangian equations with critical and supercritical phases.
From: Rulin Liu [view email]
[v1]
Wed, 27 May 2026 09:23:36 UTC (16 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。