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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.

MSC:
 47J40 Equations with nonlinear hysteresis operators 34C55 Hysteresis for ordinary differential equations 74N30 Problems involving hysteresis in solids
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