We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed Dirichlet problems. The generalized derivatives can be used to obtain a novel necessary optimality condition for the optimal control of the obstacle problem with control constraints. A comparison shows that this system is stronger than the known system of C-stationarity.

中文翻译：

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障碍问题解算子的广义导数

我们刻画了障碍问题解算子的广义导数。这种精确的表征需要使用所谓的“容量度量”理论以及宽松的Dirichlet问题的相关解算子。广义导数可用于获得新的必要最优性条件，以对具有控制约束的障碍问题进行最优控制。比较表明，该系统比已知的C平稳性系统强。