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- ItemNewton and Bouligand derivatives of the scalar play and stop operator(Les Ulis : EDP Sciences, 2020) Brokate, MartinWe prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strengthened form, and a corresponding chain rule is developed. The construction of the Newton derivative ensures that the mappings involved are measurable. © The authors. Published by EDP Sciences, 2020.
- ItemA variational inequality for the derivative of the scalar play operator(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2021) Brokate, Martin; Krejčí, PavelWe show that the directional derivative of the scalar play operator is the unique solution of a certain variational inequality. Due to the nature of the discontinuities involved, the variational inequality has an integral form based on the Kurzweil-Stieltjes integral.