论文标题
在Hermitian流形上完全非线性椭圆方程的规律性。 ii
Regularity of fully non-linear elliptic equations on Hermitian manifolds. II
论文作者
论文摘要
在本文中，我们调查了对完全非线性椭圆方程的Dirichlet问题解决方案的规律性和解决性，并在Hermitian流形上具有梯度术语，其中包括$（N-1）$ - Plurisubharmharmonic函数的Monge-ampère方程。在边界数据和边界数据上有一些规律性假设的一些显着新特征，这揭示了边界的形状如何影响这种规律性假设。这种新功能来自定量边界估计值，该估计特别使我们能够应用爆炸论点来得出梯度估计。有趣的是，当背景空间成为具有边界紧凑的riemann表面的封闭遗传学歧管的产物时，将构建亚物种。
In this paper we investigate the regularity and solvability of solutions to Dirichlet problem for fully non-linear elliptic equations with gradient terms on Hermitian manifolds, which include among others the Monge-Ampère equation for $(n-1)$-plurisubharmonic functions. Some significantly new features of regularity assumptions on the boundary and boundary data are obtained, which reveal how the shape of the boundary influences such regularity assumptions. Such new features follow from quantitative boundary estimates which specifically enable us to apply a blow-up argument to derive the gradient estimate. Interestingly, the subsolutions are constructed when the background space is moreover a product of a closed Hermitian manifold with a compact Riemann surface with boundary.
