Generalized variational inequalities. (English) Zbl 1001.49014

Krejčí, Pavel; Laurençot, Philippe

J. Convex Anal. 9, No. 1, 159-183 (2002).

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

Keywords:

hysteresis; play operator; evolution variational inequality; Young integral; essentially bounded variation; regulated functions