Research interests
My research interests lie in the qualitative properties of solutions to elliptic and parabolic PDEs, from both a variational and viscosity viewpoint. Up to now, I have mainly explored regularity theory in free boundary problems and regularity issues for PDEs in Carnot groups. Recently, I have been working on Hamilton-Jacobi-Bellman equations on graphs and oscillation estimates for Kolmogorov-type equations.
Research articles
Publications and conference proceedings
□ F. Ferrari, N. Forcillo, E. M. Merlino, Regularity for almost minimizers of a one-phase Bernoulli-type functional in Carnot Groups of step two, Calc. Var. 64, 107 (2025), no. 4, Paper No. 107, https://doi.org/10.1007/s00526-025-02959-x
□ F. Buseghin, N. Forcillo, N. Garofalo, A sub-Riemannian maximum modulus theorem, Adv. Calc. Var. 18 (2025), no. 1, 143–150, https://doi.org/10.1515/acv-2023-0066
□ F. Ferrari, N. Forcillo, Alt-Caffarelli-Friedman monotonicity formula and mean value properties in Carnot groups with applications, Boll. Unione Mat. Ital. 17 (2024), no. 2, 333–348, https://doi.org/10.1007/s40574-023-00393-5
□ S. Dipierro, F. Ferrari, N. Forcillo, E. Valdinoci, Lipschitz regularity of almost minimizers in one-phase problems driven by the p-Laplace operator, Indiana Univ. Math. J. 73 (2024), no. 3, 813–854
□ F. Ferrari, N. Forcillo, A counterexample to the monotone increasing behavior of an Alt-Caffarelli-Friedman formula in the Heisenberg group, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 34 (2023), no. 2, 295–306, 10.4171/RLM/1007
□ S. Dipierro, F. Ferrari, N. Forcillo, E. Valdinoci, On the Lipschitz regularity for almost minimizers of a one-phase Bernoulli-type functional for the p-Laplacian, Matemática Aplicada, Computacional e Industrial MACI, Vol. 9, 2023, 203-206, Proceedings of IX MACI 2023, Santa Fe, 8 al 11 de mayo de 2023
□ F. Ferrari, N. Forcillo, J. J. Manfredi, On the ∞-Laplacian on Carnot groups, J. Math. Sci. (N.Y.) 268 (2022), No. 3, 310-322, https://doi.org/10.1007/s10958-022-06198-9
□ N. Forcillo, Regularity of the free boundary in the one-phase Stefan problem: a recent approach, Bruno Pini Math. Anal. Semin., 12(1), Università di Bologna, Alma Mater Studiorum, Bologna, 2022, 122–140, https://doi.org/10.6092/issn.2240-2829/14189
□ D. De Silva, N. Forcillo, O. Savin, Perturbative estimates for the one-phase Stefan problem, Calc. Var. Partial Differential Equations 60 (2021), no.6, Paper No. 219, 38 pp., https://doi.org/10.1007/s00526-021-02003-8
□ F. Ferrari, N. Forcillo, About the existence of an Alt-Caffarelli-Friedman monotonicity formula in the Heisenberg Group, Matemática Aplicada, Computacional e Industrial MACI, Vol. 8, 2021, 301-304, Proceedings of VIII MACI 2021, Matemática Aplicada, Computacional e Industrial, La Plata, 3 al 7 de mayo de 2021
□ F. Ferrari, N. Forcillo, A new glance to the Alt-Caffarelli-Friedman monotonicity formula, Math. Eng. 2 (2020), no. 4, 657-679, https://doi.org/10.3934/mine.2020030
□ S. Dipierro, A. Dzhugan, N. Forcillo, E. Valdinoci, Enhanced boundary regularity of planar nonlocal minimal graphs and a butterfly effect, Bruno Pini Math. Anal. Semin., 11(1), Università di Bologna, Alma Mater Studiorum, Bologna, 2020, 44–67, https://doi.org/10.6092/issn.2240-2829/10585
PhD thesis
□ N. Forcillo, Regularity in degenerate elliptic and parabolic free boundary problems, 213 pp., Advisor: Fausto Ferrari, 10.48676/unibo/amsdottorato/10001
Preprints
□ N. Forcillo, J. Kitagawa, R. W. Schwab, Hamilton-Jacobi-Bellman equations on graphs, arXiv: 2511.07653
□ N. Forcillo, A. Porretta, Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations, arXiv:2510.11901, Submitted
□ F. Ferrari, N. Forcillo, D. Giovagnoli, D. Jesus, Free boundary regularity for the inhomogeneous one-phase Stefan problem, arXiv: 2404.07535, Submitted