
Journal of Convex Analysis 11 (2004), No. 1, 111130 Copyright Heldermann Verlag 2004 On Uniqueness in Evolution Quasivariational Inequalities Martin Brokate Zentrum Mathematik, Technische Universität München, 85747 Garching, Germany, brokate@ma.tum.de Pavel Krejcí Mathematical Institute, Academy of Sciences of the Czech Republic, Zitná 25, 11567 Praha 1, Czech Republic, krejci@math.cas.cz Hans Schnabel Zentrum Mathematik, Technische Universität München, 85747 Garching, Germany, schnabel@ma.tum.de We consider a rate independent evolution quasivariational inequality in a Hilbert space X with closed convex constraints having nonempty interior. We prove that there exists a unique solution which is Lipschitz dependent on the data, if the dependence of the Minkowski functional on the solution is Lipschitzian with a small constant and if also the gradient of the square of the Minkowski functional is Lipschitz continuous with respect to all variables. We exhibit an example of nonuniqueness if the assumption of Lipschitz continuity is violated by an arbitrarily small degree. Keywords: evolution quasivariational inequality, uniqueness, sweeping process, hysteresis, play operator. MSC 2000: 49J40, 34C55, 47J20. FullTextpdf (246 KB) for subscribers only. 