Abstract
We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the BV-norm and to the BV-strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.
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We are grateful to the anonymous referee for reading very carefully our manuscript.
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Open Access funding provided by Politecnico di Torino within the CRUI-CARE Agreement.
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The work of the first author was supported by the institutional support for the development of research organizations IČO 47813059. The second author is a member of GNAMPA-INdAM.
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Kopfová, J., Recupero, V. Continuity of the non-convex play operator in the space of rectifiable curves. Appl Math 68, 727–750 (2023). https://doi.org/10.21136/AM.2023.0257-22
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DOI: https://doi.org/10.21136/AM.2023.0257-22
Keywords
- evolution variational inequalities
- play operator
- sweeping processes
- functions of bounded variation
- prox-regular set