一类退化椭圆型方程Dirichlet问题的解的高阶正则性  

High Order Regularity of Solutions to the Dirichlet Problem for a Class of Degenerate Elliptic Equations

作　　者：何跃[1] 

机构地区：[1]中山大学数学与计算科学学院

出　　处：《南京师大学报（自然科学版）》2007年第1期28-32,共5页Journal of Nanjing Normal University(Natural Science Edition)

基　　金：国家自然科学基金面上基金(10571087);江苏省教育厅自然科学基金(04KJB110062)资助项目

摘　　要：由于退化椭圆型方程的研究与双曲空间中极小图的Dirichlet问题,以及曲面的无穷小等距形变刚性问题的密切联系,在有界周期域上讨论了一类退化椭圆型方程Dirichlet问题的解的高阶正则性,利用泛函分析方法得到一个涉及解的高阶正则性的充分必要条件.Since the study of degenerate elliptic equation is very closely related to the Dirichlet problem for minimal graphs in hyperbolic space and the rigidity problem arising from infinitesimal isometric deformation of surfaces, we discuss the high order regularity of solutions to the Dirichlet problem for a class of degenerate elliptic equations in a bounded periodic domain. By the methods of functional analysis, we get a sufficient and necessary condition, which concerns the high order regularity of solutions for such problems.

关 键 词：退化椭圆型方程 退化抛物型方程 有界周期区域 Dirlchlet问题 极小图 刚性问题 解的高阶正则性 

分 类 号：O175.2[理学—数学]