WIAS Preprint No. 2803, (2021)

A variational inequality for the derivative of the scalar play operator


Authors

  • Brokate, Martin
    ORCID: 0000-0003-4660-9180
  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002

2020 Mathematics Subject Classification

  • 49J40 34C55 47J20 47J40 49J42

Keywords

  • Rate independence, play operator, variational inequality, sweeping process, energetic solution, directional derivative, maximum functional, Kurzweil integral, regulated function

DOI

10.20347/WIAS.PREPRINT.2803

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.

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