# Article

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Keywords:
hysteresis operators; Preisach operator; Ishlinskii operator
Summary:
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.
References:
[1] M. A. Krasnoselskii A. V. Pokrovskii: Systems with hysteresis. (Russian) Moscow, Nauka, 1983. MR 0742931
[2] A. V. Pokrovskii: On the theory of hysteresis nonlinearities. (Russian) Dokl. Akad. Nauk SSSR 210 (1973), no. 6, 1284-1287. MR 0333869
[3] P. Krejčí: On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case. Apl. Mat. 34 (1989), 364-374. MR 1014077
[4] A. Visintin: On the Preisach model for hysteresis. Nonlinear Anal. T. M. A. 8 (1984), 977-996. MR 0760191 | Zbl 0563.35007

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