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Journal of Convex Analysis 09 (2002), No. 1, 159--184
Copyright Heldermann Verlag 2002

Generalized Variational Inequalities

Pavel Krejcí
Mathematical Institute, Academy of Sciences, Zitná 25, 11567 Praha 1, Czeck Republic

Philippe Laurencot
Mathématiques pour l'Industrie et la Physique, UMR CNRS 5640, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France

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.

Keywords: Hysteresis, evolution variational inequality, Young integral, play operator.

MSC: 34C55; 26A45, 49J40

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