Journal of Convex Analysis 19 (2012), No. 4, 1109--1139
Copyright Heldermann Verlag 2012
Differential Variational Inequalities with Locally Prox-Regular Sets
Marc Mazade
Université Montpellier 2, Dép. de Mathématiques CC 051, Place Eugène Bataillon, 34095 Montpellier, France
marc.mazade@math.univ-montp2.fr
Lionel Thibault
Université Montpellier 2, Dép. de Mathématiques CC 051, Place Eugène Bataillon, 34095 Montpellier, France
thibault@math.univ-montp2.fr
The paper studies local existence and uniqueness of absolutely continuous solutions of a differential variational inequality involving a locally prox-regular set of an infinite dimensional Hilbert space. The study requires a quantified concept of local prox-regularity termed as (r,α)-prox-regularity.
Keywords: Differential inclusions, differential variational inequalities, proximal normal cone, locally prox-regular set, (r,alpha)-prox-regular set, hypomonotonicity, sweeping process, perturbation.
MSC: 34A60, 49J52; 49J20, 58E35
[ Fulltext-pdf (248 KB)] for subscribers only.