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Generalized variational inequalities. (English) Zbl 1001.49014
Summary: We consider a rate independent evolution variational inequality with an arbitrary convex closed constraint \(Z\) in a Hilbert space \(X\). The main results consist in proving that it is well-posed in the Young integral setting in the space of functions of essentially bounded variation for every \(Z\) and in the space of regulated functions provided 0 lies in the interior of \(Z\).

MSC:
49J40 Variational inequalities
34C55 Hysteresis for ordinary differential equations
49K40 Sensitivity, stability, well-posedness
26A45 Functions of bounded variation, generalizations
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