论文标题
Lagrangian平均曲率方程的梯度估计值，具有关键和超临界阶段
Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase
论文作者
论文摘要
在本文中，如果Lagrangian阶段至关重要且超临界，并且$ c^{2} $，我们证明了拉格朗日平均曲率方程的内部梯度估计。结合[BHA21，BHA22]中证明的先验内部Hessian估计值，这解决了使用$ C^0 $边界数据的关键和超临界拉格朗日平均曲率方程的Dirichlet边界值问题。我们还为较低的规律性阶段提供了统一的梯度估计，以满足某些其他假设。
In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and $C^{2}$. Combined with the a priori interior Hessian estimates proved in [Bha21, Bha22], this solves the Dirichlet boundary value problem for the critical and supercritical Lagrangian mean curvature equation with $C^0$ boundary data. We also provide a uniform gradient estimate for lower regularity phases that satisfy certain additional hypotheses.
