Abstract We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality by a C 1 finite element method, and present the error analysis together with numerical results.

中文翻译：

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一个带点导数约束的一维椭圆分布最优控制问题

摘要 我们考虑对状态导数具有逐点约束的一维椭圆分布最优控制问题。通过利用最优状态的导数满足的变分不等式，我们在对数据进行适当假设的情况下获得最优状态的更高正则性。我们还通过C 1 有限元方法将最优控制问题求解为四阶变分不等式，并将误差分析与数值结果一起呈现。