Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions

0550720 - MÚ 2022 RIV US eng J - Journal Article
Krejčí, P. - Monteiro, Giselle Antunes - Recupero, V.
Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions.
Applied Mathematics and Optimization. Roč. 84, č. 2 (2021), s. 1477-1504. ISSN 0095-4616. E-ISSN 1432-0606
R&D Projects: GA ČR(CZ) GA20-14736S
Institutional support: RVO:67985840
Keywords : evolution variational inequalities * prox-regular sets * state-dependent sweeping processes
OECD category: Pure mathematics
Impact factor: 2.194, year: 2021
Method of publishing: Open access
https://doi.org/10.1007/s00245-021-09801-8

We show that sweeping processes with possibly non-convex prox-regular constraints generate a strongly continuous input-output mapping in the space of absolutely continuous functions. Under additional smoothness assumptions on the constraint we prove the local Lipschitz continuity of the input-output mapping. Using the Banach contraction principle, we subsequently prove that also the solution mapping associated with the state-dependent problem is locally Lipschitz continuous.
Permanent Link: http://hdl.handle.net/11104/0326018