Preprints and Publications

Preprints

1. G. Conforti, R. Kraaij, L. Tamanini and  D. Tonon, Hamilton–Jacobi equations for controlled gradient flows: existence of viscosity solutions, Preprint (2024).

2. G. Conforti, R. Kraaij and  D. Tonon, Hamilton–Jacobi equations for controlled gradient flows: cylindrical test functions, Preprint (2024).

3.  F. Salvarani and D.Tonon, Kinetic description of strategic binary games, Preprint (2017).

Publications

1. Y. Achdou, G. Carlier,  Q. Petit   and D. Tonon,  A simple city equilibrium model with an application to teleworking,  Applied Mathematics and Optimization, 28 (2) 2023

2. Y. Achdou, G. Carlier,  Q. Petit   and D. Tonon,  A Mean Field  Model for the interactions between firms on the markets of their inputs, Mathematics and Financial Economics, online first (2023).

3. G. Conforti, R. Kraaij and  D. Tonon, Hamilton-Jacobi equations for controlled gradient flows: the comparison principle, J. Funct. Anal. online first (2023).

4. F. Hérau, D. Tonon and I. Tristani, Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off, Commun.  Math. Phys., 377 (2020), pp 697-711.

5. P. J.  Graber,  A. R. Mészáros, F. J. Silva and D. Tonon, The planning problem in mean field games as a regularized mass transport, Calc. Var. Partial Diff., 58 (3) (2019), pp 115-133. 

6. M. Cirant and D. Tonon, Time-dependent focusing Mean-Field Games: the sub-critical case, Journal of Dynamics and Differential Equations, 31 (1) (2019), pp 49-79.

7. Y. Guo,  C. Kim, D. Tonon and A. Trescases, Regularity of the Boltzmann equation in convex domains, Inventiones Mathematicae, 207 (1) (2017), pp 115-290.

8. Y. Guo,  C. Kim, D. Tonon and A. Trescases, BV-Regularity of the Boltzmann equation in non-convex domains, ARMA, 220 (3) (2016), pp 1045-1093.

9. P. Cardaliaguet, A. Porretta and D. Tonon, Sobolev regularity for the first order Hamilton-Jacobi equation, Calc. Var. Partial Diff., 55 (3) (2015), pp 3037-3065. 

10. P. Cardaliaguet, J. Graber, A. Porretta and D. Tonon, Second order mean field games with degenerate diffusion and local coupling, NoDEA, 22 (5) (2015), pp 1287-1317.

11. H. Frankowska, D. Hoehener  and D. Tonon, A Second-Order Maximum Principle in Optimal Control under State Constraints, Serdica Mathematical Journal, 39 (3) (2013), pp 233-270. 

12. H. Frankowska and D. Tonon, Pointwise second-order necessary optimality conditions for the Mayer problem with control constraints, SIAM J. Control. Optim, 51 (5) (2013), pp 3814-3843.

13. H. Frankowska and D. Tonon, Inward Pointing Trajectories, Normality of the Maximum Principle and the non Occurrence of the Lavrentieff Phenomenon in Optimal Control under  State Constraints, J. Conv. Anal., 20 (4) (2013), pp 1147-1180.

14. S. Bianchini and D. Tonon, SBV regularity for Hamilton-Jacobi equations with Hamiltonian depending on (t,x),  SIAM J. Math. Anal., 44 (3) (2012), pp 2179-2203.

15. S. Bianchini and D. Tonon, SBV-like regularity for Hamilton-Jacobi equations with a convex Hamiltonian, J. Math. Anal. Appl. 391 (2012), pp 190-208.

16. D. Tonon, Some applications of the SBV Regularity Theorem for entropy solutions of  1D scalar conservation laws to ConvectionTheory and sticky particles, Riv. Mat. Univ. Parma, 3 (1) (2012), pp 163-175.

17. S. Bianchini and D. Tonon, A decomposition theorem for BV functions,  Commun. Pure Appl. Anal. (CPAA), 10 (6) (2011), pp 1549-1566.

Proceedings 

1. P. Cardaliaguet, A. Porretta and D. Tonon, A segregation problem in multi-population mean field games, Annals of ISDG, 15 (2017), pp 49-70. 

2. H. Frankowska, D. Tonon, The Goh necessary optimality conditions for the Mayer problem with control constraints, Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on, (2013), pp 538-543.

Books Chapters

1. M. S. Aronna, D. Tonon, A. Boccia, C. Martinez Campos, M. Mazzola, L. Van Nguyen, M. Palladino, T. Scarinci and F. J. Silva, Optimality Conditions (in Pontryagin Form) in  Optimal Control: Novel Directions and Applications.  Lecture Notes in Mathematics, Springer, Volume 2180, 2017, pp 1-125.

Books

1.A. Festa, D. Gomes,  F.J. Silva, and D. Tonon,  Mean Field Games: new trends and applications.  Journal of Dynamics and Games.  Volume 8 (4). AIMS, 2021.

2.D. Tonon, M.S. Aronna and D. Kalise. Optimal Control: Novel Directions and Applications.  Lecture Notes in Mathematics. Springer, Volume 2180, 2017. http://www.springer.com/fr/book/9783319607702