发表机构
School of Mathematics and Center for Nonlinear Studies, Northwest University（西北大学数学与非线性研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对特殊拉格朗日方程的外狄利克雷问题建立存在唯一性定理，推广了前人工作并改进衰减率，还求解了内狄利克雷问题，将其应用于三维二次Hessian方程的对应问题。
AI 中文摘要
我们针对特殊拉格朗日方程的外狄利克雷问题建立了存在性与唯一性定理，该方程带有无穷远处的指定渐近行为，适用于所有相的粘性解框架，以及临界和超临界相的经典解框架。这些结果推广了第二作者之前的工作，方法是移除了对渐近矩阵的限制性假设，并将衰减率改进至2-n阶。我们还求解了临界特殊拉格朗日方程的内狄利克雷问题，作为应用，在无任何容许性条件下解决了三维二次Hessian方程的所有上述对应问题。
英文摘要
We establish the existence and uniqueness theorem for the exterior Dirichlet problem for the special Lagrangian equation with prescribed asymptotic behavior at infinity, in both the viscosity setting for all the phases and classical setting for the critical and supercritical phases. These results generalize previous work by the second author by removing restrictive assumptions on the asymptotic matrix and improving the decay rate to the order $2-n$. We also solve the interior Dirichlet problem for the critical special Lagrangian equation and, as applications, all the above-mentioned corresponding problems for the three dimensional quadratic Hessian equation without any admissibility condition.
Comments27 pages
