# Continuity of hysteresis operators in Sobolev spaces

Pavel Krejčí; Vladimír Lovicar

Aplikace matematiky (1990)

- Volume: 35, Issue: 1, page 60-66
- ISSN: 0862-7940

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topKrejčí, 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 -

## References

top- M. A. Krasnoselskii A. V. Pokrovskii, Systems with hysteresis, (Russian) Moscow, Nauka, 1983. (1983) MR0742931
- A. V. Pokrovskii, On the theory of hysteresis nonlinearities, (Russian) Dokl. Akad. Nauk SSSR 210 (1973), no. 6, 1284-1287. (1973) MR0333869
- P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case, Apl. Mat. 34 (1989), 364-374. (1989) MR1014077
- A. Visintin, On the Preisach model for hysteresis, Nonlinear Anal. T. M. A. 8 (1984), 977-996. (1984) Zbl0563.35007MR0760191

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