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On locally isotone rate independent operators

✍ Scribed by Vincenzo Recupero

Publisher
Elsevier Science
Year
2007
Tongue
English
Weight
193 KB
Volume
20
Category
Article
ISSN
0893-9659

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✦ Synopsis

This note concerns rate independent operators R : Lip(0, T ) -β†’ BV (0, T ) ∩ 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 locally isotone, a slightly weaker condition than the local monotonicity well known in hysteresis. In this work 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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