| 王冠翔,张教根.关于齐次四元Monge-Amp`ere方程的一些注记*[J].数学年刊A辑,2022,43(4):445~454 |
| 关于齐次四元Monge-Amp`ere方程的一些注记* |
| Some Remarks on the Homogeneous Quaternionic Monge-Amp`ere Equations |
| Received:December 07, 2020 Revised:October 24, 2022 |
| DOI：10.16205/j.cnki.cama.2022.0029 |
| 中文关键词: 齐次四元Monge-Amp`ere方程, 极大性, 多重次调和 |
| 英文关键词:Homogeneous quaternionic Monge-Amp`ere equations, Maximality,Plurisubharmonic |
| 基金项目:中国博士后面上项目(No.2022M713057)和中国科学技术大学青年创新基金(No.WK0010000072) |
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| 中文摘要: |
| 本文考虑了四元数空间Hn中齐次四元Monge-Amp`ere方程的狄利克雷问题解的正则性.首先,当区域是边界为 C1,1 的强拟凸域时, 作者给出了解的Lipschitz估计. 其次, 考虑了四元 Monge-Amp`ere 算子的收敛性. 最后,讨论了齐次四元 Monge-Amp`ere 方程的粘性次解与F-次调和函数之间的关系. |
| 英文摘要: |
| In this paper, the authors consider the regularity of Dirichlet problem for homogeneous quaternionic Monge-Amp`ere equations in the quaternionic space Hn. The authors firstly derive a priori Lipschitz estimates when the strictly pseudoconvex domain and the boundary condition satisfy the C1,1 regularity. Secondly, the authors consider a convergence result of the quaternionic Monge-Amp`ere operators. Finally, the authors study the relations between the viscosity subsolutions of homogeneous quaternionic Monge-Amp`ere equations and F-subharmonic functions. |
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