Regularity of fully non-linear elliptic equations on Hermitian manifolds. II.
Regularity of fully non-linear elliptic equations on Hermitian manifolds. II.
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发表时间：
2020-01
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通讯作者：
Rirong Yuan
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作者：
Rirong Yuan
本文研究了Hermitian流形上带梯度项的完全非线性椭圆型方程Dirichlet问题解的正则性和可解性，其中包括$（n-1）$-多重次调和函数的Monge-Ampere方程.得到了边界和边界数据上的正则性假设的一些显著的新特征，揭示了边界的形状如何影响这些正则性假设。这样的新功能遵循定量边界估计，特别是使我们能够应用爆破参数来获得梯度估计。有趣的是，当背景空间是一个封闭的厄米特流形与一个紧的黎曼曲面与边界的乘积。
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-Ampere 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.