Continuity of hysteresis operators in Sobolev spaces

Krejčí, Pavel, and Lovicar, Vladimír. "Continuity of hysteresis operators in Sobolev spaces." Aplikace matematiky 35.1 (1990): 60-66. <http://eudml.org/doc/15610>.

@article{Krejčí1990,
abstract = {We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^\{1,p\}(0,T)$ for $1\le 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.},
author = {Krejčí, Pavel, Lovicar, Vladimír},
journal = {Aplikace matematiky},
keywords = {hysteresis operators; Preisach operator; Ishlinskii operator; hysteresis oprators},
language = {eng},
number = {1},
pages = {60-66},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuity of hysteresis operators in Sobolev spaces},
url = {http://eudml.org/doc/15610},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Lovicar, Vladimír
TI - Continuity of hysteresis operators in Sobolev spaces
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 60
EP - 66
AB - We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^{1,p}(0,T)$ for $1\le 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.
LA - eng
KW - hysteresis operators; Preisach operator; Ishlinskii operator; hysteresis oprators
UR - http://eudml.org/doc/15610
ER -