Hysteresis operators in metric spaces

Vincenzo Recupero

doi:10.3934/dcdss.2015.8.773

Article Contents

2015, Volume 8, Issue 4: 773-792. Doi: 10.3934/dcdss.2015.8.773

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Hysteresis operators in metric spaces

Vincenzo Recupero^1,

1.
Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi, 24, I 10129 Torino

Received: December 31, 2013

Revised: June 30, 2014

Published: July 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 74N30, 74C05, 34A60; Secondary: 30L99.

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