Research interests

My research interests lie in the qualitative properties of solutions to elliptic and parabolic problems. In particular, I focus on PDEs and Calculus of Variations. 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 dealing with the existence theory for elliptic operators on graphs.

Research articles

Publications

□ 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) 

□ F. Buseghin, N. Forcillo, N. Garofalo, A sub-Riemannian maximum modulus theorem, Adv. Calc. Var. 18 (2025), no. 1, 143–150

□ 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), n.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

□ F. Ferrari, N. Forcillo, Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications, Boll Unione Mat Ital (2023) 

□ F. Ferrari, N. Forcillo, Juan J. Manfredi, On the ∞-Laplacian on Carnot groups, J. Math. Sci., 268 (2022), no. 3, 310–322

□ 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

□ F. Ferrari, N. Forcillo, A new glance to the Alt-Caffarelli-Friedman monotonicity formula, Math. Eng. 2 (2020), n. 4, 657-679

Review papers

□ 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, 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

□ N. Forcillo, Regularity of the free boundary in the one-phase Stefan problem: a recent approach, Bruno Pini Mathematical Analysis Seminar, Vol. 12, n. 1, Univ.Bologna, Alma Mater Stud., Bologna, 2021, 122-140

 □ 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 

Ph. D. thesis

□ N. Forcillo, Regularity in degenerate elliptic and parabolic free boundary problems, 213 pp., Advisor: Prof. Fausto Ferrari

Submitted preprints

□ F. Ferrari, N. Forcillo, D. Giovagnoli, D. Jesus, Free boundary regularity for the inhomogeneous one-phase Stefan problem, Submitted, arXiv: 2404.07535