[back to home page - torna alla pagina principale]

links
research topics and CV
preprints
published papers
arXiv page

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

Convergence/divergence phenomena in the vanishing discount limit of Hamilton-Jacobi equations  
with Panrui Ni, Jun Yan, Maxime Zavidovique
Pre-print (November 2024).
[full paper.pdf]

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]