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BV ‐extension of rate independent operators
Author(s) -
Recupero Vincenzo
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610723
Subject(s) - mathematics , monotone polygon , extension (predicate logic) , operator (biology) , pure mathematics , space (punctuation) , monotonic function , hysteresis , operator theory , topology (electrical circuits) , discrete mathematics , mathematical analysis , combinatorics , computer science , geometry , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene , programming language , operating system
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 ) → 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 R̃: BV (0, T ) → 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 ). (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)