方程△u+f(x,u)=0的极大值原理

The Maximum Principles for the Elliptic Problem △u+f(x,u)=0

关于二阶椭圆型方程的极值原理,已经有许多结果。对于二阶非线性椭圆型方程,一般说来,通过研究解的泛函的极大值原理来对解的性质进行研究。文章对一类非线性椭圆型方程进行研究,通过构造了一种合适的泛函,得出了方程解的泛函的极大值原理。文中还对方程的各种边值问题的极大值原理进行了讨论。

There are many results about the maximum principles for second elliptic problems. In this paper, we obtain maximum principles for the functions which are defined on solutions of monlinear second order elliptic priblems . The principles can be used to estimate physical quantity.