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 from Lip(0,T) into itself, which is locally monotone and continuous with respect to the strict topology of BV admits a unique continuous extension S form BV(0,T) into itself. This result provides a general extension theorem which 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 CBV(0,T).
|Titolo:||BV-extension of rate independent operators|
|Data di pubblicazione:||2009|
|Digital Object Identifier (DOI):||10.1002/mana.200610723|
|Appare nelle tipologie:||1.1 Articolo in rivista|