2015-2025 (arxiv version in red, when available;  published version in Blue)

1. G. Bocchi, A. Porretta, Entropy-minimizing dynamical transport on Riemannian manifolds, Calc. Var. PDE (2025).

2. P. Cardaliaguet, S. Munoz, A. Porretta, Free boundary regularity and support propagation in mean field games and optimal transport, J. Math. Pures Appl. (9) 190 (2024).

3. A. Porretta, M Ricciardi, Ergodic Problems for Second-Order Mean Field Games with State Constraints, Commun. Pure Appl. Anal. 23 (2024).

4. A. Porretta, Decay rates of convergence for Fokker-Planck equations with confining drift, Adv. Math. 436 (2024).

5. P. Cardaliaguet, M. Cirant, A. Porretta, Splitting methods and short time existence for the master equations in mean field games, J. Europ. Math. Soc., 25 (2023).

6. A. Porretta, Regularizing effects of the entropy functional in optimal transport and planning problems, J. Funct. Anal., 284 (2023).

7. A. Porretta, L. Rossi, Traveling waves for a nonlocal KPP equation and mean- field game models of knowledge diffusion, Ann. I. H. Poincare -AN, 39 (2022).

8. M. Cirant, A. Porretta, Long time behavior and turnpike solutions in mildly non- monotone mean field games, ESAIM Control Optim. Calc. Var. 27 (2021).

9. A. Porretta, On the regularity of the total variation minimizers, Commun. Contemp. Math. 23 (2021).

10. F. Murat, A. Porretta, The ergodic limit for weak solutions of elliptic equations with Neumann boundary condition, Math. Eng. 3 (2021).

11. P. Cardaliaguet, M. Cirant, A. Porretta, Remarks on Nash equilibria in mean field game models with a major player, Proc. Amer. Math. Soc. 148 (2020). 

12. A. Porretta, A note on the Sobolev and Gagliardo-Nirenberg inequality when p > N , Adv. Nonlinear Stud. 20 (2020). 

13. A. Porretta, M. Ricciardi, Mean field games under invariance conditions for the state space, Comm. Partial Differential Equations 45 (2020).

14. A. Porretta, P. Souplet, Blow-up and regularization rates, loss and recovery of boundary conditions for the superquadratic viscous Hamilton-Jacobi equation, J. Math. Pures Appl. (9) 133 (2020). 

15. C. Orrieri, A. Porretta, G. Savaré, A variational approach to the mean field planning problem, J. Funct. Anal. 277 (2019). 

16. P. Cardaliaguet, A. Porretta, Long time behavior of the master equation in mean field games, Anal. PDE 12 (2019).

17. M. Magliocca, A. Porretta, Local and global time decay for parabolic equations with superlinear first order terms, Proc. Lond. Math. Soc. (3) 118 (2019).

18. Y. Achdou, A. Porretta, Mean field games with congestion, Ann. I. H. Poincar\'e -AN 35 (2018), 443-480

19. T. Leonori, A. Porretta,  On the comparison principle for unbounded solutions of elliptic equations with first order terms, J. Math. Anal. Appl.. 457 (2018)

20. A. Porretta, On the turnpike property for mean field games,  Minimax Theory Appl. 3 (2018),  285-312. 

21. A. Porretta, E. Zuazua, Numerical hypocoercivity for the Kolmogorov equation, Math. of Comp. 86 (2017), 97-119.

22. A. Porretta, P. Souplet, Analysis of the loss of boundary condition for a viscous Hamilton-Jacobi equation, Ann. I. H. Poincare -AN 34 (2017), 1913-1923.

23. A. Porretta, On the weak theory for mean field games systems, Boll. Unione Mat. Ital. 10 (2017), 411-439.

24. A. Porretta, P. Souplet,  The Profile of Boundary Gradient Blowup for the Diffusive Hamilton-Jacobi Equation,  IMRN (2016).

25. T. Leonori, A. Porretta,  Large solutions and gradient bounds for quasilinear elliptic equations, Comm. Partial Differential Equations,  41 (2016), 952-998.

26. Y. Achdou, A. Porretta,  Convergence of a finite difference scheme to weak solutions of the system of partial differential equation arising in  mean field games,  SIAM J. Numer. Anal.  54 (2016),  161-186.

27. A. Dall'Aglio, A. Porretta, Local and global regularity of weak solutions of elliptic equations with superquadratic Hamiltonian,   Trans. Amer. Math. Soc.  367 (2015),  3017-3039.

28. H. Berestycki, I. Capuzzo Dolcetta, A. Porretta, L. Rossi,  Maximum Principle and generalized principal eigenvalue for  degenerate elliptic operators, J. Math. Pures Appl. 103 (2015), 1276-1293.

29. F. Petitta, A.Porretta, On the notion of renormalized solution to nonlinear parabolic equations with general measure data, J. Elliptic and Parabolic Equations 1 (2015), 201-214.

30. A. Porretta,  Weak solutions to Fokker-Planck equations and Mean Field Games, Arch. Rational Mech. Anal. 216 (2015), 1-62.

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

32. P. Cardaliaguet, A. Porretta, D. Tonon, Sobolev regularity for the first order Hamilton-Jacobi equation, Calc. Var. Partial Differential Equations 54 (2015), 3037-3065.

33. T. Leonori, A. Porretta, G. Riey, Comparison principles for p-Laplace equations with lower order terms, Ann. Mat. Pura Appl. (2016), 1-27.

Selected papers (2000 - 2015):

• N. Grenon, F. Murat, A. Porretta,  A  priori estimates and existence  for elliptic equations  with gradient dependent terms,  Ann. Scuola Normale Sup. Pisa Cl. Sci. (V)}  XIII (2014), 137--205.

• A. Porretta, E. Zuazua, Long time versus steady state optimal control, Siam J. Control Optimization 51 n. 6 (2013), 4242--4273.

• A. Porretta, E. Priola, Global Lipschitz regularizing effects for linear and nonlinear parabolic equations, J. Math. Pures Appl. (9) 100 (2013), 633--686

• P. Cardaliaguet, J.-M. Lasry, P.-L. Lions, A. Porretta,  Long time average of mean field games with a nonlocal coupling, Siam J. Control Optimization 51 n. 5 (2013)

• P. Cardaliaguet, J.-M. Lasry, P.-L. Lions, A. Porretta,  Long time average of mean field games, Network Heter. Media 7 (2012), n.2,  279--301

• F. Petitta, A.C. Ponce, A. Porretta,  Diffuse measures and nonlinear parabolic equations, J. Evol. Equ.  11 (2011), 861--905.

• T. Leonori, A. Porretta, Gradient bounds for elliptic problems singular at the boundary, Arch. Rat. Mech. Anal. 202 (2011), 663--705

• I. Capuzzo Dolcetta, F. Leoni, A. Porretta,  Holder estimates for degenerate elliptic  equations with coercive Hamiltonians,  Trans. Amer. Math. Soc.  362 (2010), 4511--4536.

• A. Porretta,  The "ergodic limit" for a viscous Hamilton-Jacobi equation with Dirichlet conditions, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl.  21 (2010), 59--78.

• G. Barles, A. Porretta, T. Tabet Tchamba,  On the Large Time Behavior of Solutions of the Dirichlet problem for Subquadratic Viscous Hamilton-Jacobi Equations, J. Math. Pures Appl. 94 (2010),  497--519. 

• A. Porretta, L. Veron, Separable p-harmonic functions in a cone and related quasilinear equations on manifolds, J. European Math. Soc. 11 (2009), 1285--1305.

• T. Leonori, A. Porretta,  The boundary behavior of blow-up solutions related to a  stochastic control problem with state constraint, Siam J. Math. Anal. 39 (2007/08),  1295--1327.

• A. Porretta, L. Veron, Symmetry of large solutions of nonlinear elliptic equations in a  ball, J. Funct. Anal. 236 (2006), 581--591

• D.  Blanchard, A. Porretta,  Stefan problems with nonlinear diffusion and convection, J. Diff. Equations 210 (2005), 383--428

• J. Droniou, A. Porretta, A. Prignet, Parabolic capacity and soft measures  for nonlinear equations,  Potential Analysis 19 (2003),  99-161.

• C. Mascia, A. Porretta, A. Terracina, Nonhomogeneous Dirichlet problems for degenerate parabolic--hyperbolic equations, Arch. Ration. Mech. Anal. 163 (2002), 87--124.