Journal
JOURNAL OF DIFFERENTIAL EQUATIONS
Volume 226, Issue 1, Pages 135-179Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jde.2005.12.005
Keywords
differential inclusions; sweeping process; perturbation; prox-regular set; normal cone; map of bounded variation; radon measure; absolutely continuous map; set-valued map
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This paper is devoted to the study of differential inclusions, particularly discontinuous perturbed sweeping processes in the infinite-dimensional setting. On the one hand, the sets involved are assumed to be prox-regular and to have a variation given by a function which is of bounded variation and right continuous. On the other hand, the perturbation satisfies a linear growth condition with respect to a fixed compact subset. Finally, the case where the sets move in an absolutely continuous way is recovered as a consequence. (c) 2006 Elsevier Inc. All rights reserved.
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