Abstract
The sweeping process was introduced and solved in the Lipschitz case (and some other cases, but under “metric hypotheses”) by J. J. Moreau [30, 31, 391 (for an intuitive presentation see Section 1). Then after preliminary papers by H. Tanaka [47] and C. Castaing [ 14,151, M. D. P. Monteiro Marques [26,27] solved the problem when the multifunction is right lower semi-continuous and contains a ball. The aim of this paper is to give another proof of the Monteiro Marques result using an interior lipschitzean approximation of the multifunction. Our result is slightly less general because we are obliged to assume bilateral lower semi-continuity and left closedness of the graph. But this is a different approach and it is an opportunity to detail some useful preliminaries (for more details see the complete exposure [49]).
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