关于齐次四元Monge-Ampère方程的一些注记  

Some Remarks on the Homogeneous Quaternionic Monge-Ampère Equations

作　　者：王冠翔 张教根 WANG Guanxiang;ZHANG Jiaogen(School of Mathematical Sciences,University of Science and Technology of Chi na,Hefei 230026,China)

机构地区：[1]中国科学技术大学数学科学学院,合肥230026

出　　处：《数学年刊（A辑）》2022年第4期445-454,共10页Chinese Annals of Mathematics

基　　金：中国博士后面上项目(No.2022M713057);中国科学技术大学青年创新基金(No.WK0010000072)的资助。

摘　　要：本文考虑了四元数空间Hn中齐次四元Monge-Ampère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MongeAmpère算子的收敛性.最后,讨论了齐次四元Monge-Ampère方程的粘性次解与F-次调和函数之间的关系.In this paper,the authors consider the regularity of Dirichlet problem for homogeneous quaternionic Monge-Ampere 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 C1,1regularity.Secondly,the authors consider a convergence result of the quaternionic Monge-Ampere operators.Finally,the authors study the relations between the viscosity subsolutions of homogeneous quaternionic Monge-Ampere equations and F-subharmonic functions.

关 键 词：齐次四元Monge-Ampère方程 极大性 多重次调和 

分 类 号：O174.4[理学—数学]