Geodesic
Existence and Relaxation of BV Solutions for a Sweeping Process with a Nonconvex-Valued Perturbation
Journal of convex analysis, Tome 27 (2020) no. 2, pp. 645-672
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We study a measurable sweeping process with a multivalued perturbation in a separable Hilbert space. The values of the perturbation are closed, not necessarily convex sets. The retraction of the sweeping process is bounded by a positive Radon measure. A solution of the sweeping process is a pair consisting of a right continuous function of bounded variation whose differential measure is absolutely continuous with respect to some positive Radon measure and an integrable selector of the perturbation considered along this function. The density of the differential measure with respect to the Radon measure above satisfies the corresponding inclusion.
Classification : 28B20, 49J45, 49J53
Mots-clés : Function of bounded variation, Radon measure, differential measure, density of a measure, BV solutions, existence theorem, relaxation theorem 
@article{JCA_2020_27_2_JCA_2020_27_2_a11,
     author = {S. A. Timoshin and A. A. Tolstonogov},
     title = {Existence and {Relaxation} of {BV} {Solutions} for a {Sweeping} {Process} with a {Nonconvex-Valued} {Perturbation}},
     journal = {Journal of convex analysis},
     pages = {645--672},
     year = {2020},
     volume = {27},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a11/}
}
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S. A. Timoshin; A. A. Tolstonogov. Existence and Relaxation of BV Solutions for a Sweeping Process with a Nonconvex-Valued Perturbation. Journal of convex analysis, Tome 27 (2020) no. 2, pp. 645-672. http://geodesic.mathdoc.fr/item/JCA_2020_27_2_JCA_2020_27_2_a11/