Recent publications
Preprints:
• F.Camilli, Li-Yau inequality and related properties on metric
star graphs, arXiv:2501.12685
• F.Camilli,
C.Marchi, C.Mendico, A note on first order quasi-stationary Mean Field
Games, arXiv:2409.18483
• F.Camilli, A.Festa,
L.Marzufero, A network
model for urban planning, arXiv:2408.05140
To appear
• J.Berry, F.Camilli, Stationary
Mean Field Games on networks with sticky transition conditions,
to appear on ESAIM Control Optim. Calc. Var.
• F.Camilli,
M.Lauriere, Q.Tang, Learning
equilibria
in Cournot mean field games of controls, to appear on
SIAM J. of Control
& Optimization
• F.Camilli, A.Goffi, C.Mendico, Qualitative and quantitative properties for
Hamilton-Jacobi equations via nonlinear adjoint method, to
appear on Annali della Scuola Normale Superiore di Pisa, Classe di
Scienze
• 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 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.