Generalized derivatives for the solution operator of the obstacle problem

Anne-Therese Rauls; Gerd Wachsmuth

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arXiv · 1806.05052

Generalized derivatives for the solution operator of the obstacle problem

Anne-Therese Rauls·Gerd Wachsmuth

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Abstract

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.

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Anne-Therese Rauls, Gerd Wachsmuth. 2018-06-13. Generalized derivatives for the solution operator of the obstacle problem. https://arxiv.org/abs/1806.05052

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