Research / CV

Research topics

Hamilton-Jacobi-Bellman equations, Mean Field Control and Mean Field Games, fully nonlinear PDEs.

Monographs

with F. R. Harvey, H. B. Lawson, K. R. Payne: Comparison Principles for General Potential Theories and PDEs,  Annals of Mathematics Studies series, Princeton University Press, 2023

Papers

+ with G. Verzini: Local Hölder and maximal regularity of solutions of elliptic equations with superquadratic gradient terms, Advances in Mathematics, 2022

+ with P. Cardaliaguet and A. Porretta: Splitting methods and short time existence for the master equation in mean field games, J. Eur. Math. Soc. (JEMS), 2022

+ with A. Porretta: Long time behaviour and turnpike solutions in mildly non-monotone mean field games, ESAIM Contol Optim. Calc. Var., 2021

+ with D. Ghilli: Existence and non-existence for time-dependent mean field games with strong aggregation, Math. Annalen, 2021

+ with A. Goffi: Maximal Lq-regularity for parabolic Hamilton-Jacobi equations and applications to Mean Field Games, Annals of PDE, 2021

+ with A. Goffi: On the problem of maximal Lq-regularity for viscous Hamilton-Jacobi equations, Arch. Ration. Mech. Anal., 2021

+ with D. Gomes, E. Pimentel, H. Sanchez-Morgado: On some singular Mean-Field Games, J. Dyn. Games, 2021

+ with A. Cesaroni: Brake orbits and heteroclinic connections for first order Mean Field Games, Trans. Amer. Math. Soc., 2021

+ with A. Cesaroni: 1-dimensional multi-agent optimal control with aggregation and distance constraints: qualitative properties and mean-field limit,  Nonlinearity, 2021

+ with K. R. Payne: Comparison principles for viscosity solutions of elliptic branches of fully nonlinear equations independent of the gradient, Mathematics in Engineering, 2021.

+ with P. Cardaliaguet, A. Porretta: Remarks on Nash equilibria in mean field game models with a major player, Proc. Amer. Math. Soc, 2020.

+ with A. Goffi: Lipschitz regularity for viscous Hamilton-Jacobi equations with L^p terms. Ann. Inst. H. Poincaré (C), 2020.

+ with R. Gianni, P. Mannucci: Short time existence for a general backward-forward parabolic system arising from MFG. Dyn. Games Appl., 2020.

+ with A. Goffi: On the existence and uniqueness of solutions to time-dependent fractional MFG. SIAM J. Math. Anal., 2019.

+ On the existence of oscillating solutions in non-monotone Mean-Field Games. J. Differential Equations, 2019.

+ with A. Cesaroni: Concentration of ground states in stationary MFG systems. Analysis & PDE, 2019.

+ with L. Nurbekyan: The variational structure and time-periodic solutions for mean-field games systems. Minimax Theory Appl., 2018.

+ with D. Tonon: Time-dependent focusing Mean-Field Games: the sub-critical case. J. Dynam. Differential Equations , 2018.

+ with A. Cesaroni, S. Dipierro, M. Novaga, E. Valdinoci: On stationary fractional mean field games.  J. Math. Pures Appl., 2018.

+ with K. R. Payne: On viscosity solutions to the Dirichlet problem for elliptic branches of nonhomogeneous fully nonlinear equations. Publ. Mat., 2017.

+ with G. Verzini: Bifurcation and segregation in quadratic two-populations Mean Field Games systems. ESAIM Control Optim. Calc. Var., 2017. 

+ with Y. Achdou and M. Bardi: Mean Field Games models of segregation. Math. Models Methods Appl. Sci., 2017.

+ Stationary focusing Mean Field Games. Comm. Partial Differential Equations, 2016.

+ A generalization of the Hopf-Cole transformation for stationary Mean Field Games systems. C. R. Math. Acad. Sci. Paris, 2015.

+ The dirichlet problem for prescribed principal curvature equations. Nonlinear Differ. Equ. Appl., 2014. 

+ Multi-population mean field games systems with neumann boundary conditions. J. Math. Pures Appl., 2014.

+ On the solvability of some ergodic control problems in Rd. SIAM J. Control Optim.,  2014.

Proceedings

+ with A. Goffi: On the Liouville property for fully nonlinear equations with superlinear first-order terms, to appear in Proceedings of the Conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, AMS Contemporary Mathematics (CONM) book series. 

+ with M. Bardi: Uniqueness of solutions in MFG with several populations and Neumann conditions. PDE Models for Multi-Agent Phenomena - Springer Indam Series, 2019.

+ with A. Cesaroni: Introduction to variational methods for viscous ergodic Mean-Field Games with local coupling. Contemporary Research in Elliptic PDEs and Related Topics - Springer Indam Series, 2019.

You can find (most of) my works and recent preprints on arXiv !!