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\(BV\) solutions of rate independent variational inequalities. (English) Zbl 1229.49012

Summary: We prove a theorem providing a geometric characterization of \(BV\) continuous vector rate independent operators. We apply this theorem to rate independent evolution variational inequalities and deduce new continuity properties of their solution operator: the vectorial play operator.

MSC:

49J40 Variational inequalities
47J35 Nonlinear evolution equations
74C15 Large-strain, rate-independent theories of plasticity (including nonlinear plasticity)
34C55 Hysteresis for ordinary differential equations
26A45 Functions of bounded variation, generalizations
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