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
Published
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 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.
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, arXiv: 2310.15949 (2023), to appear in Indiana University Mathematics Journal.
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, 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.
Preprints
Interpolated time-Hölder regularity of solutions of fully nonlinear parabolic equations, arXiv:2406.12427 (2024), submitted for publication.
with G. Tralli. Global geometric estimates for the heat equation via duality methods, arXiv: 2409.15456 (2024), submitted for publication.
Remarks on the rate of convergence of the vanishing viscosity process of Hamilton-Jacobi equations, arXiv: 2412.15651 (2024), submitted for publication.
Rate of convergence of the vanishing viscosity method for Hamilton-Jacobi equations with Neumann boundary conditions, arXiv: 2509.01973 (2025), submitted for publication.
with A. Cecchin. Convergence rates for the vanishing viscosity approximation of fully nonlinear, non-convex, second-order Hamilton-Jacobi equations via nonlinear convolutions, arXiv: 2509.12144 (2025), submitted for publication.