Generalized derivatives for the solution operator of the obstacle problem
Optimization and Control
2018-06-14 v1
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.
Cite
@article{arxiv.1806.05052,
title = {Generalized derivatives for the solution operator of the obstacle problem},
author = {Anne-Therese Rauls and Gerd Wachsmuth},
journal= {arXiv preprint arXiv:1806.05052},
year = {2018}
}