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On a class of scalar variational inequalities with measure data. (English) Zbl 1177.74308
Summary: We consider a class of variational inequalities defining the so-called hysteresis play operator. We propose a new approach to discontinuous $$BV$$-solutions based on measure theoretical arguments, which enable us to infer the existence of solutions as a simple consequence of the classical theory. In this way, we generalize a recent result where only continuous $$BV$$-solutions were studied. We also provide a representation formula which allows to deduce the continuity of the play operator from general theorems on hysteresis operators.

##### MSC:
 74N30 Problems involving hysteresis in solids 74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) 34C55 Hysteresis for ordinary differential equations 26A45 Functions of bounded variation, generalizations
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