Research interests
Regularity theory and qualitative properties for elliptic and parabolic equations; Hamilton-Jacobi equations; Transport- and advection-diffusion equations; Fully nonlinear equations; Mean Field Games.
Publications
Research articles
with M. Cirant. On the existence and uniqueness of solutions to time-dependent fractional MFG, SIAM Journal on Mathematical Analysis 51 (2019), no. 2, 913-954, DOI: 10.1137/18M1216420 .
with M. Bardi. New strong maximum and comparison principles for fully nonlinear degenerate elliptic PDEs, Calculus of Variations and Partial Differential Equations, 58 (2019), no. 6, 184, DOI: 10.1007/s00526-019-1620-2 .
with M. Cirant. Lipschitz regularity for viscous Hamilton-Jacobi equations with L^p terms, Annales de l'Institut Henri Poincaré C, Analyse Non Linéaire, 37 (2020), no. 4, 757-784, DOI: 10.1016/j.anihpc.2020.01.006 .
with F. Camilli. Existence and regularity results for viscous Hamilton-Jacobi equations with Caputo time-fractional derivative, Nonlinear Differential Equations and Applications (NoDEA), 27 (2020), no. 2, 22, DOI: 10.1007/s00030-020-0624-0 .
Some new Liouville-type results for fully nonlinear PDEs on the Heisenberg group, Nonlinear Analysis, 200 (2020), 112013, DOI: 10.1016/j.na.2020.112013 .
with F. Pediconi. A note on the strong maximum principle for fully nonlinear equations on Riemannian manifolds, The Journal of Geometric Analysis 31 (2021), no. 8, 8641-8665, DOI: 10.1007/s12220-021-00607-2 .
with M. Cirant. On the problem of maximal L^q-regularity for viscous Hamilton-Jacobi equations, Archive for Rational Mechanics and Analysis 240 (2021), no. 3, 1521-1534, DOI: 10.1007/s00205-021-01641-8 .
Transport equations with nonlocal diffusion and applications to Hamilton-Jacobi equations, Journal of Evolution Equations 21 (2021), 4261-4317, DOI: 10.1007/s00028-021-00720-3 .
with S. Cacace and F. Camilli. A policy iteration method for Mean Field Games, ESAIM: Control, Optimisation and Calculus of Variations 27 (2021), 85, DOI: 10.1051/cocv/2021081.
with M. Cirant. Maximal L^q-regularity for parabolic Hamilton-Jacobi equations and applications to Mean Field Games, Annals of PDE 7 (2021), 19, DOI: 10.1007/s40818-021-00109-y.
with M. Bardi. Liouville results for fully nonlinear equations modeled on Hörmander vector fields: I. The Heisenberg group, Mathematische Annalen 383 (2022), no. 1-2, 171-201, DOI: 10.1007/s00208-020-02118-x .
with F. Pediconi. Sobolev regularity for nonlinear Poisson equations with Neumann boundary conditions on Riemannian manifolds, Forum Mathematicum 35, no.2 (2023), 431-456, DOI: 10.1515/forum-2022-0119.
with M. Bardi. Liouville results for fully nonlinear equations modeled on Hörmander vector fields: II. Carnot groups and Grushin geometries, Advances in Differential Equations 28, no. 7-8 (2023), 637-684, DOI: 10.57262/ade028-0708-637.
Hölder regularity and Liouville properties for nonlinear elliptic inequalities with power-growth gradient terms, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 153 (2023), 1833-1857, DOI: 10.1017/prm.2022.72 .
On the optimal L^q-regularity for viscous Hamilton-Jacobi equations with subquadratic growth in the gradient, Communications in Contemporary Mathematics 26 (2024), no. 6, 2350019, DOI: 10.1142/S0219199723500190 .
High-order estimates for fully nonlinear equations under weak concavity assumptions, Journal de Mathématiques Pures et Appliquées 182 (2024), 223-252, DOI: 10.1016/j.matpur.2023.12.006.
Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions, Bulletin of the London Mathematical Society 56 (2024), 1385-1398, DOI: 10.1112/blms.13001.
A priori Lipschitz estimates for nonlinear equations with mixed local and nonlocal diffusion via the adjoint-Bernstein method, Bollettino dell'Unione Matematica Italiana 17 (2024), 373-390, DOI: 10.1007/s40574-022-00340-w.
with T. Leonori. On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method 76 (2025), no. 6, Indiana University Mathematics Journal, 1607-1643, DOI: 10.1512/iumj.2025.74.60515.
On the strong maximum principle for fully nonlinear parabolic equations of second order, Proceedings of the American Mathematical Society 153 (2025) 1575-1583, DOI: 10.1090/proc/17050.
with F. Camilli and C. Mendico. Quantitative and qualitative properties for Hamilton-Jacobi PDEs via the nonlinear adjoint method, arXiv: 2307.12932 (2023), to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 30, DOI: 10.2422/2036-2145.202404_015.
Interior Hölder and Calderón-Zygmund estimates for fully nonlinear equations with natural gradient growth, Journal of Functional Analysis 288 (2025) 110800, DOI: 10.1016/j.jfa.2024.110800.
with M. Cirant and T. Leonori, Gradient estimates for quasilinear elliptic Neumann problems with unbounded first-order terms, arXiv: 2211.03760 (2022), to appear in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, DOI: 10.2422/2036-2145.202411_006.
with M. Cirant, Convergence rates for the vanishing viscosity approximation of Hamilton-Jacobi equations: the convex case, arXiv: 2502.15495 (2025), to appear in Indiana University Mathematics Journal.
On the smoothness of solutions of fully nonlinear second order equations in the plane, 7 (2026), no. 14, Partial Differential Equations and Applications, DOI: 10.1007/s42985-026-00378-x.
Rate of convergence of the vanishing viscosity method for Hamilton-Jacobi equations with Neumann boundary conditions, arXiv: 2509.01973 (2025), to appear in Journal of Hyperbolic Differential Equations.
Interpolated time-Hölder regularity of solutions of fully nonlinear parabolic equations, arXiv:2406.12427 (2024), to appear in Bulletin des Sciences Mathématiques, DOI: 10.1016/j.bulsci.2026.103807.
Remarks on the rate of convergence of the vanishing viscosity process of Hamilton-Jacobi equations, Nonlinearity, 39 (2026), 035026, DOI: 10.1088/1361-6544/ae5201.
with A. Cecchin. Convergence rates for the vanishing viscosity approximation of fully nonlinear, non-convex, second-order Hamilton-Jacobi equations via nonlinear convolutions, Calculus of Variations and Partial Differential Equations, 65 (2026), no. 174, DOI: 10.1007/s00526-026-03341-1.
Proceedings
with M. Cirant. On the Liouville property for fully nonlinear equations with superlinear first-order terms, "Proceedings of the Conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs", Contemporary Mathematics, American Mathematical Society, 781 (2023), DOI: 10.1090/conm/781/15707.
Surveys
Quantitative maximal L^2-regularity for viscous Hamilton-Jacobi PDEs in 2D and Mean Field Games, arXiv: 2603.09515 (2026).
Preprints
with G. Tralli. Global geometric estimates for the heat equation via duality methods, arXiv: 2409.15456 (2024), submitted for publication.
with G. Giovannardi. Transport-diffusion equations with irregular data and applications to stability estimates for second-order Hamilton-Jacobi PDEs, arXiv: 2602.07969 (2026).