Geodesic
Convex Valued Geodesics and Applications to Sweeping Processes with Bounded Retraction
Journal of convex analysis, Tome 27 (2020) no. 2, pp. 535-556
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We provide a formulation for sweeping processes with arbitrary locally bounded retraction, not necessarily left or right continuous. Moreover we provide a proof of the existence and uniqueness of solutions for this formulation which relies on the reduction to the 1-Lipschitz continuous case by using a suitable family of geodesics for the asymmetric Hausdorff-like distance called excess.
Classification : 34G25, 34A60, 47J20, 74C05
Mots-clés : Evolution variational inequalities, functions of bounded variation, sweeping processes, convex sets, retraction, geodesics with respect to the excess 
@article{JCA_2020_27_2_JCA_2020_27_2_a6,
     author = {V. Recupero},
     title = {Convex {Valued} {Geodesics} and {Applications} to {Sweeping} {Processes} with {Bounded} {Retraction}},
     journal = {Journal of convex analysis},
     pages = {535--556},
     year = {2020},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a6/}
}
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V. Recupero. Convex Valued Geodesics and Applications to Sweeping Processes with Bounded Retraction. Journal of convex analysis, Tome 27 (2020) no. 2, pp. 535-556. http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a6/