Sweeping process by prox-regular sets in Riemannian Hilbert manifolds

2015/01/28 by Frédéric Bernicot, Bernicot, Frédéric, Juliette Venel +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Metric Geometry (math.MG) #math.AP #math.MG

paper · pdf · doi:10.48550/arxiv.1501.07207

27 pages

arxiv created 2015/01/28 · arxiv updated 2015/01/29

Abstract

In this paper, we deal with sweeping processes on (possibly infinite-dimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the framework of such manifolds. Especially we introduce the concept of local prox-regularity of a closed subset in accordance with the geometrical features of the ambient manifold and we check that this regularity implies a property of hypomonotonicity for the proximal normal cone. Moreover we show that the metric projection onto a locally prox-regular set is single-valued in its neighborhood. Then under some assumptions, we prove the well-posedness of perturbed sweeping processes by locally prox-regular sets.

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