A variational inequality for the derivative of the scalar play operator

Martin Brokate; Pavel Krejčí

doi:10.23952/jano.3.2021.2.03

A variational inequality for the derivative of the scalar play operator

Martin Brokate
, Pavel Krejčí

Lehrstuhl für Numerische Mathematik / Steuerungstheorie (2008 — 2025)

Weierstrass Institute for Applied Analysis and Stochastics
Faculty of Civil Engineering

Publikation: Beitrag in Fachzeitschrift › Artikel › Begutachtung

1 Zitat (Scopus)

Abstract

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.

Originalsprache	Englisch
Seiten (von - bis)	263-283
Seitenumfang	21
Fachzeitschrift	Journal of Applied and Numerical Optimization
Jahrgang	3
Ausgabenummer	2
DOIs	https://doi.org/10.23952/jano.3.2021.2.03
Publikationsstatus	Veröffentlicht - Aug. 2021

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10.23952/jano.3.2021.2.03

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title = "A variational inequality for the derivative of the scalar play operator",

abstract = "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.",

keywords = "Energetic solution, Rate independence, Regulated function, Sweeping process, Variational inequality",

author = "Martin Brokate and Pavel Krej{\v c}{\'i}",

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AB - 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.

KW - Energetic solution

KW - Rate independence

KW - Regulated function

KW - Sweeping process

KW - Variational inequality

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A variational inequality for the derivative of the scalar play operator

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