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Hysteresis operators in metric spaces

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  • Motivated by the sweeping processes, we develop an abstract theory of continuous hysteresis operators acting between rectifiable curves with values in metric spaces. In particular we study the continuity properties of such operators and how they can be extended from the space of Lipschitz continuous functions to the space of rectifiable curves. Applications to the sweeping processes and to the vector play operator are shown.
    Mathematics Subject Classification: Primary: 74N30, 74C05, 34A60; Secondary: 30L99.


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