Journal of Convex Analysis 11 (2004), No. 1, 111--130
Copyright Heldermann Verlag 2004
On Uniqueness in Evolution Quasivariational Inequalities
Zentrum Mathematik, Technische Universität München, 85747 Garching, Germany, firstname.lastname@example.org
Mathematical Institute, Academy of Sciences of the Czech Republic, Zitná 25, 11567 Praha 1, Czech Republic, email@example.com
Zentrum Mathematik, Technische Universität München, 85747 Garching, Germany, firstname.lastname@example.org
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.
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