Recent publications
Preprints:
• F.Camilli,
M.Lauriere, Q.Tang,Learning
equilibria in Cournot mean field games of controls,
arXiv:2405.01812
• F.Camilli, A.Goffi, C.Mendico, Qualitative
and quantitative properties for Hamilton-Jacobi equations via
nonlinear adjoint method, arXiv:2307.12932
To
appear
• F.Camilli,Q.Tang, On the quadratic convergence of the Newton's method for Mean Field Games with non-separable Hamiltonians, to appear on Dynamic Games and Appl.
• F.Camilli, A. Festa, A system of Hamilton-Jacobi equations characterizing geodesic centroidal tessellations, to appear on Communications on Applied Mathematics and Computation
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 Analysis 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.