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

Recupero, Vincenzo

Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 10, No. 2, 269-315 (2011).

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

Keywords:

geometric characterization; \(BV\) continuous vector rate independent operators; evolution variational inequalities; vectorial play operator