退化秩为0的二阶椭圆型方程的边值问题(英文)

Boundary Value Problems for Second Order Elliptic Equations with Degenerate Rank 0

许多作者提出和讨论了二阶退化椭圆型方程的一些边值问题,如Dirichlet边值问题和混合边值问题.本文讨论高维区域中退化秩为0的二阶椭圆型方程的一些边值问题,这些问题包括上述问题作为特殊情况.先给出这些问题的提法,然后使用列紧性原理和极值原理证明了上述二阶椭圆型方程边值解的存在性和唯一性.

Many authors posed and discussed some boundary value problems,mainly the Dirichlet problem and mixed boundary value problem for second order elliptic equations with parabolic degeneracy.In this paper some boundary value problems for the degenerate elliptic equations of second order are discussed in a high dimensional domain,which include the above problems as a special case.Fristly the boundary value problems for the equations is formulated,and then by using the compactness principle, the existence of solutions for the above problems is proved.