Existence of sweeping process in Banach spaces under directional prox-regularity

2008/12/26 by Frédéric Bernicot, Frederic Bernicot, Bernicot, Frederic +2 · 1 citation
Computer Science · Mathematics · #34A60 #49J52 #58C20. #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #math.CA #math.FA #msc:34A60 #msc:49J52 #msc:58C20.

paper · pdf · doi:10.48550/arxiv.0812.4673

33 pages

openalex publication_date 2008/12/26 · arxiv created 2009/03/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is devoted to weaken "classical" assumptions and give new arguments to prove existence of sweeping process (associated to the proximal normal cone of sets). Mainly we define the concept of a "directional prox-regularity" and give assumptions about a Banach space to insure the existence of such sweeping process (which permit to generalize the existing results requiring a Hilbertian structure).

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• Numerical scheme for a whole class of sweeping process

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