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.
Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions / Recupero, Vincenzo. - In: APPLIED MATHEMATICS AND OPTIMIZATION. - ISSN 0095-4616. - STAMPA. - 84:Supplement issue 2(2021), pp. 1477-1504. [10.1007/s00245-021-09801-8]
Titolo: | Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions | |
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Data di pubblicazione: | 2021 | |
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Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00245-021-09801-8 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
File in questo prodotto:
File | Descrizione | Tipologia | Licenza | |
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prox-ac_REV.pdf | Articolo | 2. Post-print / Author's Accepted Manuscript | ![]() | Visibile a tuttiVisualizza/Apri |
Krejčí2021_Article_ExplicitAndImplicitNon-convexS.pdf | Articolo | 2a Post-print versione editoriale / Version of Record | ![]() | Visibile a tuttiVisualizza/Apri |
http://hdl.handle.net/11583/2909732