We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^{1,p}(0,T)$ for $1\leq p < +\infty$, (localy) Lipschitz continuous in $W^{1,1}(0,T)$ and discontinuous in $W^{1,\infty}(0,T)$ for arbitrary $T>0$. Examples show that this result is optimal.
@article{104387,
author = {Pavel Krej\v c\'\i\ and Vladim\'\i r Lovicar},
title = {Continuity of hysteresis operators in Sobolev spaces},
journal = {Applications of Mathematics},
volume = {35},
year = {1990},
pages = {60-66},
zbl = {0705.47054},
mrnumber = {1039411},
language = {en},
url = {http://dml.mathdoc.fr/item/104387}
}
Krejčí, Pavel; Lovicar, Vladimír. Continuity of hysteresis operators in Sobolev spaces. Applications of Mathematics, Tome 35 (1990) pp. 60-66. http://gdmltest.u-ga.fr/item/104387/
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