Archivio Istituzionale della RicercaThis note concerns rate independent operators R from Lip(0,T) to BV(0,T), with R(Lip(0,T)) contained in C(0,T), that are continuous with respect to the strict metric of BV. In a recent paper we proved that R can be continuously extended to all of BV(0,T) provided it is local isotone, a slightly weaker condition than local monotonicity well-known in hysteresis. In this paper we prove that local isotony is also a necessary condition, thereby giving a characterization of rate independent operators R that admit a continuous extension to BV.
On locally isotone rate independent operators / Recupero, Vincenzo. - In: APPLIED MATHEMATICS LETTERS. - ISSN 0893-9659. - STAMPA. - 20:(2007), pp. 1156-1160. [10.1016/j.aml.2006.10.006]
On locally isotone rate independent operators
RECUPERO, VINCENZO
2007
Abstract
This note concerns rate independent operators R from Lip(0,T) to BV(0,T), with R(Lip(0,T)) contained in C(0,T), that are continuous with respect to the strict metric of BV. In a recent paper we proved that R can be continuously extended to all of BV(0,T) provided it is local isotone, a slightly weaker condition than local monotonicity well-known in hysteresis. In this paper we prove that local isotony is also a necessary condition, thereby giving a characterization of rate independent operators R that admit a continuous extension to BV.
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https://hdl.handle.net/11583/1485380
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