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Newton and Bouligand derivatives of the scalar play and stop operator
2020, Brokate, Martin
We 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.
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A variational inequality for the derivative of the scalar play operator
2021, Brokate, Martin, Krejčí, Pavel
We 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.