@misc{RaulsWachsmuth, author = {Rauls, Anne-Therese and Wachsmuth, Gerd}, title = {Generalized Derivatives for the Solution Operator of the Obstacle Problem}, series = {Set-Valued and Variational Analysis}, volume = {28}, journal = {Set-Valued and Variational Analysis}, number = {2}, issn = {1877-0533}, doi = {10.1007/s11228-019-0506-y}, pages = {259 -- 285}, 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.}, language = {en} }