Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions
Dynamical Systems
2021-06-29 v3 Analysis of PDEs
Abstract
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.
Cite
@article{arxiv.2005.10942,
title = {Explicit and implicit non-convex sweeping processes in the space of absolutely continuous functions},
author = {Pavel Krejci and Giselle Antunes Monteiro and Vincenzo Recupero},
journal= {arXiv preprint arXiv:2005.10942},
year = {2021}
}
Comments
Some comments have been added; Acknowledgment and Bibliogrphy sections have been expanded. To appear in "Applied Mathematics and Optimization"