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Article

Kopfová, Jana ; Recupero, Vincenzo
Continuity of the non-convex play operator in the space of rectifiable curves. (English). Applications of Mathematics, vol. 68 (2023), issue 6, pp. 727-750
MSC: 34A60, 34G25, 47J20, 49J52, 74C05 | MR 4669928 | Zbl 07790544 | DOI: 10.21136/AM.2023.0257-22
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Keywords:
evolution variational inequalities; play operator; sweeping processes; functions of bounded variation; prox-regular set
Summary:
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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