拟线性椭圆变分不等式的障碍最优控制问题

Optimal Control of Quasilinear Elliptic Obstacle Problems

对拟线性椭圆变分不等式的障碍最优控制问题(即以障碍为控制变量)进行了研究．指标泛函为Lagrange型,其中含有控制变量二阶导数的p次幂,这使得最优性条件的推导颇为不易．对所考虑的问题给出了最优控制的存在性定理以及必要条件．

This paper considers an optimal control problem for a quasilinear elliptic obstacle variational inequality in which the obstacle is taken as the control. The cost functional of this optimal control problem is of Lagrange type in which the p-th power of Laplacian of the control appears. This feature leads that it is hard to derive the optimality system for the underlying problem. And the existence and optimality system for the optimal control are established.