Preprints and recent articles

Mathscinet                          Scopus                    Web of Sciences  

Preprints:

• A. Basti, J. Berry, F. Camilli, Markov Chain Approximation of Sticky Diffusions and Hamilton-Jacobi-Bellman Equations on Networks, arXiv2607.26709.

• F. Ancona, A. Basti, F. Camilli, Kolmogorov $\varepsilon$-entropy of numerical solutions for scalar conservation laws with convex flux, arXiv:2605.07427.

• F. Camilli, C. Mendico, Semi-Discrete Approximation of Aubry and Mather sets, arXiv:2604.24148 

To appear

• A. Basti, F. Camilli, A.Festa,  A Mean Field Games Perspective on Evolutionary Clustering, Applied Mathematical Modelling.

• A. Basti, F. Camilli, $L^p$ Estimates for Numerical Approximation of Hamilton--Jacobi Equations, Numerische Mathematik

• F .Camilli, A.Goffi, C. Mendico, Qualitative and quantitative properties for Hamilton-Jacobi equations via nonlinear adjoint method,  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze.

2026

• F. Camilli, Q.Tang,Y.-S. Zhou, A semi-Lagrangian method for solving state constraint Mean Field Games in Macroeconomics,   SIAM J. Control Optim. 64 (2026), 3443--3469.

• F. Camilli, A. Festa, L. Marzufero, Approximation of viscous transport and conservative equations with one sided Lipschitz velocity fields,  SIAM J. Numer. Anal. 64 (2026), 1043-1071

• F. Camilli, A. Festa, L. Marzufero, A network model for urban planning, J. Optim. Theory Appl. 209 (2026), no. 1, Paper No. 33.

2025

• Q.Tang, F. Camilli, Y.-S. Zhou, Yong-Shen, Policy iteration method for discounted infinite horizon mean field games: the semi-Lagrangian approach. Sci. China Inf. Sci. 68 (2025), no. 11, Paper No. 210206.

• F. Camilli, Li-Yau inequality and related properties on metric star graphs,  Potential Anal. 63 (2025), no. 2, 885–893.

• F. Camilli, C.Marchi, C.Mendico, A note on first order quasi-stationary Mean Field Games, Comm.Math.Sci.,   23 (2025),  no. 6, 1729–1740.

• F. Camilli, Q.Tang, On the quadratic convergence of the Newton's method for Mean Field Games with non-separable Hamiltonians, Dyn. Games Appl. 15 (2025), no. 2, 534–557.

• F. Camilli, M.Lauriere, Q.Tang, Learning equilibria in Cournot mean field games of controls, SIAM J. Control Optim. 63 (2025), no. 2, 1407–1431.

• J. Berry, F.Camilli, Stationary Mean Field Games on networks with sticky transition conditions,   ESAIM Control Optim. Calc. Var. 31 (2025), Paper No. 18.

• F. Camilli, A. Festa, A system of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, Communications on Applied Mathematics and Computation 7 (2025), 289-314.

2024

• F. Camilli, C. Marchi, A continuous dependance estimate for viscous Hamilton-Jacobi equations on on networks with applications, Calc. Var. Partial Differential Equations 63 (2024), no. 1, paper No. 18.

2023

• S.Cacace, F.Camilli, Approximation of the value function for optimal control problems on stratified domains, SIAM J. Numer. Anal. 61 (2023), no. 3, 1172-1194.

• F.Camilli, C. Marchi, On quasi-stationary Mean Field Games of controls, Appl. Math. Optim. 87 (2023), no. 3, 47.

2022

• F. Camilli, C. Marchi, A note on Kazdan-Warner equation on networks, Adv. Calc. Var. 15 (2022), no. 4,693-704.

• F.Camilli, Q.Tang, Rates of convergence for the policy iteration method for Mean Field Games systems, J. Math. Anal. Appl. 512 (2022), no. 1, Paper No. 126138.

2021
• F.Camilli, S.Duisembay, Q. Tang, Approximation of an optimal control problem for the time-fractional Fokker-Planck equation, J. Dyn. Games 8 (2021),381-402.
• S.Cacace, F.Camilli, A.Goffi, A policy iteration method for Mean Field Games, ESAIM Control Optim. Calc. Var., 27 (2021), paper No. 85, 19 pp.
• L.Aquilanti, S.Cacace, F.Camilli, R.De Maio, A Mean Field Games approach to cluster analysis, Appl. Math. Optim. 84 (2021), 299-323.
• F. Camilli, A quadratic Mean Field Games model for the Langevin equation, Axioms 10 (2021), 68.
• L.Aquilanti, S.Cacace, F.Camilli, R.De Maio, A Mean Field Games model for mixtures of Bernoulli and categorical distributions, J. Dyn. Games 8 (2021), 35-59.
• F.Camilli, G.Cavagnari, R.De Maio, B.Piccoli, Superposition principles and schemes for measure differential equations, Kinet. Relat. Models 14 (2021), 89-113.

2020
• F.Camilli, S.Duisembay, Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative, Minimax Theory Appl. 5 (2020), no. 2, 199-220.
• Q. Tang, F.Camilli,Variational time-fractional Mean Field Game, Dyn. Games Appl. 10(2020),573-588.
• F.Camilli, A.Goffi, Existence and regularity results for viscous Hamilton-Jacobi equations with Caputo time-fractional derivative, NoDea Nonlinear Differential Equations Appl. 27 (2020), no.2, paper No. 22.

2019
• S.Cacace, F.Camilli, R.De Maio, A.Tosin, A measure theoretic approach to traffic flow optimization on networks, European J. of Appl. Math. 30 (2019), 1187-1209.
• F.Camilli, R.De Maio, Memory effects in measure transport equations, Kinet. Relat. Models 12 (2019), 1229-1245.
• F.Camilli, R.De Maio, A time-fractional Mean Field Game, A dv.Differential Equations, 24 (2019), 531-554.
• F.Camilli, R.De Maio, E.Iacomini, A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time derivative, J. Math. Anal. Appl., 477(2019), 1019-1032.

2018
• S.Cacace, F. Camilli, A. Cesaroni, C. Marchi, An ergodic problem for Mean Field Games: qualitative properties and numerical simulations, Minimax Th. Appl., 3 (2018), no.2, 211-226.
• F. Camilli, E.Carlini, C. Marchi, A flame propagation model on a network with application to a blocking problem, Discrete Contin. Dyn. Syst. Ser.S. 11 (2018), no.5, 825-843.
• F.Camilli, R.De Maio, A.Tosin, Measure-valued solutions to nonlocal transport equations on network J.Differential Equations 264 (2018), no. 12, 7213-7241.
• S.Cacace, F. Camilli, L.Corrias, A differential model for growing sandpiles on networks, SIAM J. Math. Anal. 50 (2018), 2509–2535.
Software: SPNET (Sand Pile on NETworks)

2017
• F. Camilli, S.Tozza, A unified approach to the well-posedness of some non-Lambertian models in Shape-from-Shading theory, SIAM J. Imaging Sciences 10 (2017), 26-46.
• F.Camilli, R.De Maio, A.Tosin, Tranport of measures on networks, Netw. Heterog. Media 12 (2017), no. 2, 191-215.
• F. Camilli, A.Festa, S.Tozza, A discrete Hughes' model for pedestrian flow on graphs
Netw. Heterog. Media 12 (2017), no. 1, 93–112.
• F.Camilli, R. Capitanelli, M. A.Vivaldi, Absolutely Minimizing Lipschitz Extensions and Infinity Harmonic Functions on the Sierpinski gasket, Nonlinear Anal. 163 (2017), 71-85.
• F. Camilli, L.Corrias, Parabolic models for chemotaxis on weighted networks, J. Math. Pures Appl 108 (2017), 459-480.
• I.Birindelli, F. Camilli, I.Capuzzo Dolcetta, On the approximation of the principal eigenvalue for a class of nonlinear elliptic operators, Comm. Math. Sci., 15 (2017), 55-75.
•S.Cacace, F. Camilli, C. Marchi, A numerical method for Mean Field Games on networks, ESAIM: Math. Model. and Num. Anal., 51 (2017), 63–88.

2016
• F. Camilli, C. Marchi, Stationary Mean Field Games systems defined on networks, SIAM J. of Control & Optimization, 54 (2016), no. 2, 1085–1103.
• S.Cacace, F. Camilli, A generalized Newtom method for homogenization of Hamilton-Jacobi equations, SIAM J. Sci. Comput., Vol. 38 (2016), No. 6, A3589-A3617.
• F. Camilli, R.Capitanelli, C. Marchi, Eikonal equations on the Sierpinski gasket,
Math. Ann. 364 (2016), 1167-1188.

2015
• F. Camilli, E.Carlini, C. Marchi, A model problem for Mean Field Games on networks, Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4173--4192.

2014
• Y. Achdou, F. Camilli, L.Corrias, On numerical approximation of the Hamilton-Jacobi-transport system arising in high frequency approximations, Discrete Contin. Dyn. Syst-Ser.B 19 (2014), no.3, 629-650.

2013
•F. Camilli, D.Schieborn, Viscosity solutions of Eikonal equations on topological networks, Calc. Var. Partial Differential Equations 46 (2013), no.3, 671--686
• F. Camilli, C. Marchi, D.Schieborn, The vanishing viscosity limit for Hamilton-Jacobi equation on networks, J.Differential Equations 254 (2013), no.10, 4122-4143
• Y. Achdou, F. Camilli, A. Cutrì, N. Tchou, Hamilton-Jacobi equations constrained on networks, NoDea Nonlinear Differential Equations Appl. 20 (2013), 413--445.
• F. Camilli, D.Schieborn, C. Marchi, Eikonal equations on ramified spaces,
Interfaces and Free Boundaries 15 (2013), 121–140
• F. Camilli, C. Marchi, A comparison among various notions of viscosity solutions for Hamilton-Jacobi equations on networks, J. Math. Anal. Appl. 407 (2013), 112–118
• F.Camilli, A.Festa e D.Schieborn, An approximation scheme for a Hamilton-Jacobi equation defined on a network, Applied Num. Math. 73 (2013), 33-47.
• Y.Achdou, F.Camilli, I.Capuzzo Dolcetta, Mean field games: convergence of a finite difference method, SIAM J. Numer. Anal. 51 (2013), 2585-2612.

2012
• Y.Achdou, F.Camilli, I.Capuzzo Dolcetta, Mean field games: numerical methods for the planning problem, SIAM J. of Control & Optimization 50 (2012), 77-109.
• A.Briani, F. Camilli, H. Zidani, Approximation schemes for monotone systemsof nonlinear second order partial differential equations: convergence result and error estimate, Differ. Equ. Appl., 4 (2012), 297-317.
• F.Camilli,C.Marchi, Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations, Nonlinear Analysis TMA, 75 (2012), 5103-5118.
• F.Camilli, O.Ley, P.Loreti e V.Nguyen, Large time behavior of weakly coupled systems of first-order Hamilton-Jacobi equations, NoDEA Nonlinear Differential Equations Appl. 19 (2012), no. 6, 719–749.
• F.Camilli, F.Silva, A semi-discrete in time approximation for a model first order-finite horizon mean field game problem, Network & Heterogeneous Media, 7 (2012), 263-277.