A Bernstein problem for special Lagrangian equations in exterior domains
A Bernstein problem for special Lagrangian equations in exterior domains
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外域特殊拉格朗日方程的伯恩斯坦问题
DOI：
10.1016/j.aim.2019.106927
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发表时间：
2020
影响因子：
1.7
通讯作者：
Yu Yuan
中科院分区：
文献类型：
--
作者：
Dongsheng Li;Zhisu Li;Yu Yuan
建立了具有超临界相或半凸性的特殊拉格朗日方程的解在外部区域上的二次渐近性。“凸”情形的方法是基于一般完全非线性椭圆型方程的“外”Evans-Krylov或外Liouvle型结果，该结果趋向于有界Hessian的常渐近性，以及某些旋转变元趋于Hessian界。我们的统一方法还导致了外部区域上的Monge-Ampère方程(已知)、二次Hessian方程和逆调和Hessian方程的凸解的二次渐近。半凸的情形是基于Allard-Almgren关于切锥的唯一性。
We establish quadratic asymptotics for solutions to special Lagrangian equations with supercritical phases or with semiconvexity on solutions in exterior domains. The method for “convex” case is based on an “exterior” Evans-Krylov or exterior Liouville type result for general fully nonlinear elliptic equations toward constant asymptotics of bounded Hessian, and also certain rotation arguments toward Hessian bound. Our unified approach also leads to quadratic asymptotics for convex solutions to Monge-Ampère equations (previously known), quadratic Hessian equations, and inverse harmonic Hessian equations over exterior domains. The semiconvex case is based on Allard-Almgren's uniqueness of tangent cones.