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Sobolev and strict continuity of general hysteresis operators. (English) Zbl 1214.47081
Summary: The most natural and important topologies connected with hysteresis operators are those induced by uniform convergence, \(W^{1,1}\)-convergence, and strict convergence. Indeed, the supremum norm and the variation are invariant under reparameterization. We prove a general result that implies that, if a hysteresis operator is continuous with respect to the topology of \(W^{1,1}\), then it is continuous with respect to the strict topology.

47J40 Equations with nonlinear hysteresis operators
34C55 Hysteresis for ordinary differential equations
74N30 Problems involving hysteresis in solids
Full Text: DOI
[1] Krasnosel’skii, Systems with Hysteresis (1989)
[2] Mayergoyz, Mathematical Models of Hysteresis (1991)
[3] Visintin, Applied Mathematical Sciences 111 (1994)
[4] Brokate, Applied Mathematical Sciences 121 (1996)
[5] Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations (1996)
[6] Recupero, BV-extension of rate independent operators, Mathematische Nachrichten 282 (1) pp 86– (2009) · Zbl 1168.47049
[7] Recupero, On locally isotone rate independent operators, Applied Mathematics Letters 20 pp 1156– (2007) · Zbl 1152.47059
[8] Rudin, Real and Complex Analysis (1966)
[9] Ambrosio, Functions of Bounded Variation and Free Discontinuity Problems (2000) · Zbl 0957.49001
[10] Brezis, Analyse Fonctionelle-Théorie et Applications (1983)
[11] Federer, Geometric Measure Theory (1969) · Zbl 0176.00801
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