Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|Number of page(s)||34|
|Published online||11 November 2020|
Newton and Bouligand derivatives of the scalar play and stop operator
Department of Mathematics, Technical University of Munich,
2 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany.
* Corresponding author: firstname.lastname@example.org
Accepted: 6 April 2020
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.
Mathematics Subject Classification: 47H30 / 47J40 / 49J52 / 49M15 / 58C20
Key words: Rate independence / hysteresis operator / Newton derivative / Bouligand derivative / play, stop / sensitivity / maximum functional / variational inequality / measurable selector / semismooth / chain rule
© The authors. Published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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