半线性椭圆方程支配系统的最优性条件

Optimiality Condition for a Class of Semi-Linear Elliptic Equations

本文讨论了可能具有多值解的椭圆型偏微分方程支配系统的最优控制问题，我们通过构造一个抛物方程控制问题的逼近序列，并利用抛物方程控制问题的结果，得到了椭圆系统最优控制的必要条件．

We study the optimal control problem for a class of elliptic equations that may possess multiple solutions. By constructing a sequence of parabolic control problems and using the results for the parabolic control problems, we obtain necessary conditions for optimal control of the elliptic equation.