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Department of Mathematics, University of Roma
Centro di ricerca matematica E. De Giorgi

Viscosity, Variational and Control Theoretic Methods for Hamilton-Jacobi (HJ) equations, weak KAM Theory, asymptotic problems for HJ equations.

cv in english     cv in italian

Stochastic homogenization of HJ equations: a differential game approach  
with Raimundo Saona, Bruno Ziliotto
Pre-print (June 2024).
[full paper.pdf]

Stochastic homogenization of nondegenerate viscous HJ equations in 1d  
Pre-print (February 2024).
[full paper.pdf]

Stochastic homogenization of quasiconvex degenerate viscous HJ equations in 1d  
Calc. Var. Partial Differential Equations, to appear.
[full paper.pdf]

Stochastic homogenization of nonconvex viscous Hamilton-Jacobi equations in one space dimension  
with Elena Kosygina, Atilla Yilmaz
Comm. Partial Differential Equations 49 (2024), no. 7-8, 698-734.
[full paper.pdf]

Stochastic homogenization of a class of quasiconvex and possibly degenerate viscous HJ equations in 1d  
J. Convex Anal. 31 (2024), no. 2, 477-496
[full paper.pdf]

Discrete approximation of stochastic Mather measures  
with Renato Iturriaga, Jose Luis Perez Garmendia, Juan Carlos Pardo, Hector Sanchez Morgado
Proc. Amer. Math. Soc. (in press).
[full paper.pdf]

On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case  
with Italo Capuzzo-Dolcetta
Comm. Partial Differential Equations 48 (2023), no. 4, 576-622
[full paper.pdf]

Stochastic homogenization of a class of nonconvex viscous HJ equations in one space dimension
with Elena Kosygina
J. Differential Equations 333 (2022), 231-267
[full paper.pdf]

Discrete approximation of the viscous HJ equation  
with Hitoshi Ishii, Renato Iturriaga, Hector Sanchez Morgado
Stoch. Partial Differ. Equ. Anal. Comput. 9 (2021), no. 4, 1081-1104
[full paper.pdf]

Convergence of the solutions of discounted Hamilton-Jacobi systems  
with Maxime Zavidovique
Adv. Calc. Var. 14 (2021), no. 2, 193-206
[full paper.pdf]

On the vanishing discount problem from the negative direction  
with Lin Wang
Discrete Contin. Dyn. Syst. 41 (2021), no. 5, 2377-2389
[full paper.pdf]

Existence and uniqueness of solutions to parabolic equations with super-linear Hamiltonians.  
Commun. Contemp. Math. 21 (2019). no. 1
[full paper.pdf]

Random Lax-Oleinik semigroups for Hamilton-Jacobi systems  
with Antonio Siconolfi and Maxime Zavidovique
J. Math. Pures Appl. (9) 120 (2018), 294-333
[full paper.pdf]

Homogenization of viscous and non-viscous HJ equations: a remark and an application  
with Elena Kosygina
Calc. Var. Partial Differential Equations, 56 (2017), no. 4, 56-95.
[full paper.pdf]

Convergence of the solutions of the discounted equation: the discrete case  
with Albert Fathi, Renato Iturriaga, Maxime Zavidovique
Mathematische Zeitschrift 284 (2016), no. 3-4, 1021-1034.
[full paper.pdf]

Convergence of the solutions of the discounted Hamilton-Jacobi equation  
with Albert Fathi, Renato Iturriaga, Maxime Zavidovique
Inventiones Mathematicae 206 (2016), no. 1, 29-55.
[full paper.pdf]

Existence and regularity of strict critical subsolutions in the stationary ergodic setting  
with Antonio Siconolfi
Annales de l'Institut Henri Poincare / Analyse non lineaire 33 (2016), no. 2, 243-272
[full paper.pdf]

On the (non) existence of viscosity solutions of multi-time Hamilton-Jacobi equations  
with Maxime Zavidovique
J. Differential Equations 258 (2015), no. 2, 362-378.
[full paper.pdf]

Aubry sets for weakly coupled systems of Hamilton-Jacobi equations  
with Maxime Zavidovique
SIAM J. Math. Anal. 46 (2014), no. 5, 3361-3389.
[full paper.pdf]

Weak KAM theory for nonregular commuting Hamiltonians  
with Maxime Zavidovique
Discrete Contin. Dyn. Syst. Ser. B 18, 1 (2013)
[full paper.pdf]

Weak KAM Theory topics in the stationary ergodic setting 
with Antonio Siconolfi
Calc. Var. Partial Differential Equations 44, 3-4 (2012), 319-350
[full paper.pdf]

Metric techniques for convex stationary ergodic Hamiltonians  
with Antonio Siconolfi
Calc. Var. Partial Differential Equations 40, 3-4 (2011), 391-421
[full paper.pdf]

Exact and approximate correctors for stochastic Hamiltonians: the 1-dimensional case  
with Antonio Siconolfi
Math. Ann. 345, 4 (2009), 749-782
[full paper.pdf]

Integral representation of abstract functionals of autonomous type  
Proc. Roy. Soc. Edinburgh Sect. A 138, 4 (2008), 725-754
[full paper.pdf]

Homogenization of two-phase metrics and applications  
with Marcello Ponsiglione
J. Anal. Math. 103 (2007), 157-196
[full paper.pdf]

Bolza problems with discontinuous Lagrangians and Lipschitz-continuity of the value function
SIAM J. Control Optim. 46, 5 (2007), 1897-1921
[full paper.pdf]

A generalized dynamical approach to the large time behavior of solutions of Hamilton-Jacobi equations  
with Antonio Siconolfi
SIAM J. Math. Anal. 38, 2 (2006), 478-502
[full paper.pdf]

Monge solutions for discontinuous Hamiltonians  
with Ariela Briani
ESAIM Control Optim. Calc. Var. 11, 2 (2005), 229-251
[full paper.pdf]

Smooth approximation of weak Finsler metrics  
Differential Integral Equations 18, 5 (2005), 509-530
[full paper.pdf]

On the relaxation of a class of functionals defined on Riemannian distances  
J. Convex Anal. 12, 1 (2005), 113-130
[full paper.pdf]

Optimal Riemannian distances preventing mass transfer  
with Giuseppe Buttazzo, Ilaria Fragalà, Fabricio Macià
J. Reine Angew. Math. 575 (2004), 157-171
[full paper.pdf]

On calibrations for Lawson's cones  
Rend. Sem. Mat. Univ. Padova 111 (2004), 55-70
[full paper.pdf]