论文标题
在Hermitian流形上完全非线性椭圆方程的规律性
Regularity of fully non-linear elliptic equations on Hermitian manifolds
论文作者
论文摘要
在本文中，我们提出了新的见解和想法，以建立解决方案的定量边界估计值，以解决与真实的分析Levi平面边界的紧凑型Hermitian歧管上的一类完全非线性椭圆方程的问题。借助手头的定量边界估计，我们可以建立梯度估计值，并提供统一的方法来研究Dirichlet问题解决方案的存在和规律性，并具有足够平滑的边界数据，其中包括Kähler指标空间中的地球方程。我们的方法也可以应用于与凹边界紧凑的Riemannian歧管上的类似非线性椭圆方程的Dirichlet问题。
In this paper we propose new insights and ideas to set up quantitative boundary estimates for solutions to Dirichlet problem of a class of fully non-linear elliptic equations on compact Hermitian manifolds with real analytic Levi flat boundary. With the quantitative boundary estimates at hand, we can establish the gradient estimate and give a unified approach to investigate the existence and regularity of solutions of Dirichlet problem with sufficiently smooth boundary data, which include the geodesic equation in the space of Kähler metrics as a special case. Our method can also be applied to Dirichlet problem for analogous fully non-linear elliptic equations on a compact Riemannian manifold with concave boundary.
