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Existence and Relaxation of BV Solutions for a Sweeping Process with a Nonconvex-Valued Perturbation

Авторы: Timoshin S.A., Tolstonogov A.A.

Журнал: Journal of Convex Analysis

Том: 27

Номер: 2

Год: 2020

Отчётный год: 2020

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Аннотация: 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. Along with the original perturbation, we consider the perturbation with the convexified values. We prove theorems on the existence and relaxation of solutions. The latter means the density of the solution set of the sweeping process with the original perturbation in the solution set of the sweeping process with the convexified perturbation. These solution sets are considered as subsets of the Cartesian product of the space of right continuous functions of bounded variation and the space of integrable functions. These spaces are endowed with the topology of uniform convergence on an interval and the weak topology, respectively.

Индексируется WOS: Q4

Индексируется Scopus: Нет

Индексируется УБС: Нет

Индексируется РИНЦ: Нет

Индексируется ВАК: Нет

Индексируется CORE: Нет

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