Preprints and recent publications

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 Applications
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, Adv.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 an 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.