超临界相位的Special Lagrangian方程的狄利克雷边值问题  

THE DIRICHLET PROBLEM OF A SPECIAL LAGRANGIAN TYPE EQUATION WITH SUPERCRITICAL PHASE

作　　者：朱圣 ZHU Sheng(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《数学杂志》2022年第6期482-492,共11页Journal of Mathematics

基　　金：National Natural Science Foundation of China(12171260).

摘　　要：在这篇文章中,我们介绍了一种Special Lagrangian方程,并且研究此方程在超临界相位时对应的狄利克雷边值问题.通过建立整体的C 2估计,运用经典的连续性方法得到解的存在性.In this paper,we introduce a special Lagrangian type operator,and consider the corresponding Dirichlet problem of the special Lagrangian type equation with supercritical phase.By establishing the global C 2 estimates,we obtain the existence theorem of classical solutions by the method of continuity.

关 键 词：Special Lagrangian方程 狄利克雷问题 超临界相位 

分 类 号：O175.25[理学—数学]