平面上一类超定问题

A Class of Overdetermined Problem in the Plane

主要讨论平面上一类超定方程解存在的必要性问题。研究了函数的拉普拉斯算子不等于-1,而是等于一般的函数,在边界上同时满足Dirichlet条件和Neumann条件,证明在某些条件下这类超定方程有解的必要条件是它的区域是平面上的圆。

The existence of a class of overdetermined equations in the plane were discussed in this thesis.The Laplace of a function was not equal to -1, but was equal to the general function.It also satisfied the Dirichlet condition and Neumann condition on the boundary.It was proved that under some condtions the necessary condition of the existence of the solution for this overdetermined equation is that its region is a round in the plane.