title: Epi-Lipschitzian reachable sets of differential inclusions
creator: Lorenz, Thomas
subject: ddc-510
subject: 510 Mathematics
description: The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well-known assumptions of Filippov's existence theorem (about differential inclusions), every epi-Lipschitzian initial compact set (of the Euclidean space) preserves this regularity for a (possibly short) time, i.e. its reachable set is also epi-Lipschitzian for all small times. The proof is based on Rockafellar's geometric characterization of epi-Lipschitzian sets and uses a new result about the "inner semicontinuity" of Clarke tangent cone (to reachable sets) with respect to both time and base point.
date: 2007
type: Preprint
type: info:eu-repo/semantics/preprint
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/7351/1/Lorenz_epiLipschitz_reachable_sets_revised.pdf
identifier: DOI:10.11588/heidok.00007351
identifier: urn:nbn:de:bsz:16-opus-73514
identifier:   Lorenz, Thomas  (2007) Epi-Lipschitzian reachable sets of differential inclusions.  [Preprint]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/7351/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: ger