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Author

A. Tolstonogov

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Open access 2020

Compactness of BV Solutions of a Convex Sweeping Process of Measurable Differential Inclusion

A measurable sweeping process with a multivalued perturbation is considered in a separable Hilbert space. The retraction of the sweeping process is a function of bounded variation whose differential measure is absolutely continuous with respect to a positive Radon measure. The values of the multivalued perturbation are...

A. Tolstonogov · 8 citations · ⚡2
Open access 2020

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

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 c...

S. Timoshin, A. Tolstonogov · 3 citations
Open access 2025

BV Solutions of a State-Dependent Prox-Regular Sweeping Process with Nonconvex Perturbations

In a separable Hilbert space, we consider a sweeping process with perturbation. The values of the moving set are prox-regular sets dependent on time and state. The variation of the moving set is controlled in the state in a Lipschitz way and in time by a positive Radon measure. The perturbation is the sum of two multiv...

A. Tolstonogov · 0 citations

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