%0 Generic
%A Lorenz, Thomas
%D 2007
%F heidok:7351
%K Differential inclusion , reachable set (alias attainable set) , epi-Lipschitzian sets , Clarke tangent cone
%R 10.11588/heidok.00007351
%T Epi-Lipschitzian reachable sets of differential inclusions
%U https://archiv.ub.uni-heidelberg.de/volltextserver/7351/
%X 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.