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BV -extension of rate independent operators

✍ Scribed by Vincenzo Recupero

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
191 KB
Volume
282
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Rate independent operators naturally arise in the mathematical analysis of hysteresis. Among rate independent operators, the locally monotone ones are those better suited for the study of PDE's with hysteresis. We prove that a rate independent operator R: Lip (0, T) β†’ BV (0, T) ∩ C (0, T) which is locally monotone and continuous with respect to the strict topology of BV admits a unique continuous extension RΜƒ: BV (0, T) β†’ BV (0, T). This general result applies to several concrete hysteresis operators. For many of these operators the existence of a continuous extension was previously known at most to the space BV (0, T) ∩ C (0, T). (Β© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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