Publications

• Capuani, R., Marigonda, A. , Ricciardi, M. Random Lift of Set Valued Maps and Applications to Multiagent Dynamics. Set-Valued Var. Anal 31, 28 (2023). https://doi.org/10.1007/s11228-023-00693-0, 2023

•  Capuani, R., Marigonda, A., A Mean Field Model For Counter CBRN Threats, accepted to appear in Lecture Notes in Computer Science, Springer.

• Capuani, R., Marigonda, A., Constrained Mean Field Games Equilibria as Fixed Point of Random Lifting of Set-Valued Maps, IFAC-PapersOnLine, Volume 55, Issue 30, Pages 180 - 185, DOI: 10.1016/j.ifacol.2022.11.049, 2022.

• Capuani, R., Marigonda, A., Mogentale, M., Random Lifting of Set-Valued Maps,  In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127., Springer, Cham. http://doi.org/10.1007/978-3-030-97549-4_34, 2022

• Cannarsa, P., Capuani, R. & Cardaliaguet, P. Mean field games with state constraints: from mild to pointwise solutions of the PDE system. Calc. Var. 60, 108, https://doi.org/10.1007/s00526-021-01936-4, 33 pages, 2021.

•  Capuani, R., Dutta, P., Nguyen, K. T., Metric entropy for functions of bounded total generalized variation, SIAM J. Math. Anal., 53(1), DOI: 10.1137/20M1310953, 22 pages, 2021.

•  Capuani, R., Gilmore, S., Nguyen, K. T., A model of debt with bankruptcy risk and currency devaluation, Minimax Theory and its Applications , 5, no. 2, 23 pages, 2020.

•  Cannarsa, P.,Capuani, R., and Cardaliaguet, P., C^{1,1}-smoothness of constrained solutions in the calculus of variations with application to mean field games,Mathematics in Engineering,1(1), 29 pages, doi:10.3934/Mine.2018.1.174, 2018.

•  Cannarsa, P., Capuani, R., Existence and uniqueness for Mean Field Games with state constraints,"PDE models for multi-agent phenomena", P. Cardaliaguet, A.Porretta, F. Salvarani editors, Springer INdAM Series, 22 pages, 2018.

Submitted, Preprints 

1. Capuani, R., Marigonda, A., M. Quincampoix, Set-driven evolution for multiagent system, submitted.

2.  Bagagiolo, F., Capuani, R., Marzufero, L., A single player and a mass of agents: a pursuit evasion-like game,https://arxiv.org/abs/2302.05742 , submitted.

3.  Capuani, R., Di Persio, L., Kondratiev, Y., Ricciardi, M., da Silva, J.L., Random time dynamical system, https://arxiv.org/pdf/2108.05261.pdf, preprint.

Work in Progress

1. with A. Marigonda,  A model for multi-agent system with visibility constraints.

2.with A. Marigonda and A. Briggi (MSc student), Methods of mean field control in S.A.R. operations

Thesis

1.  Mean Field Games with state constraints,  Ph.D. Thesis Tor Vergata University (Rome, Italy) and Paris-Dauphine University (Paris, France), 2018

2. De Giorgi regularity theorem and nonlinear potential theory, M. Sc. Thesis  Federico II University, Naples, Italy, 2014

3. Linear stability for the linear methods multistep, B. Sc. Thesis Federico II University, Naples, Italy, 2011