Geodesic
Continuity of hysteresis operators in Sobolev spaces
Applications of Mathematics, Tome 35 (1990) no. 1, pp. 60-66

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MR Zbl
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.
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.
DOI : 10.21136/AM.1990.104387
Classification : 46E35, 47H30, 58C07, 73E50, 73E99, 74H15, 74H99
Keywords: hysteresis operators; Preisach operator; Ishlinskii operator 
Krejčí, Pavel; Lovicar, Vladimír. Continuity of hysteresis operators in Sobolev spaces. Applications of Mathematics, Tome 35 (1990) no. 1, pp. 60-66. doi: 10.21136/AM.1990.104387
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[3] P. Krejčí: On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case. Apl. Mat. 34 (1989), 364-374. | MR

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