关于 Hermitian 流形上完全非线性椭圆方程 Dirichlet 问题的正则性
偏微分方程分析
2022-03-10 v1 微分几何
摘要
通过在下调和假设下建立边界估计的定量版本，我们导出了 Hermitian 流形上可能具有退化右端项的完全非线性椭圆方程 Dirichlet 问题的可解性与正则性。此外，当背景流形是闭 Hermitian 流形与带边紧 Riemann 曲面的乘积时，我们构造了该下调和。
引用
@article{arxiv.2203.04898,
title = {On the regularity of Dirichlet problem for fully non-linear elliptic equations on Hermitian manifolds},
author = {Rirong Yuan},
journal= {arXiv preprint arXiv:2203.04898},
year = {2022}
}
备注
The main context of this paper is the integration of [arXiv:2203.03439] and the first parts of [arXiv:2001.09238] and [arXiv:2106.14837], while the second parts ofthe posts [arXiv:2001.09238, arXiv:2106.14837] are reorganized into another paper. More precisely, this paper is essentially extracted from [arXiv:2203.03439], Sections 4-6 in [arXiv:2001.09238] and Section 3 in [arXiv:2106.14837]