Preprints
P. Bonicatto, P. Lahti, E. Pasqualetto, A topological characterization of indecomposable sets of finite perimeter (2025) arXiv: 2512.18319
P. Bonicatto, A general Frobenius' Theorem via the Transport of Currents (2025) arXiv: 2510.21478
P. Bonicatto, F. Rindler, and H. Turnbull, The Space-Time Connectivity Theorem for Normal Currents (2025) arXiv: 2510.08360
P. Bonicatto and G. Del Nin, Well-posedness of the transport of normal currents by time-dependent vector fields (2025) arXiv: 2504.15974
P. Bonicatto and F. Rindler, Homogenization of elasto-plastic evolutions driven by the flow of dislocations (2024) arXiv: 2410.02906
S. Bianchini, P. Bonicatto, and E. Marconi, A Lagrangian approach for scalar multi-dimensional conservation laws (2017)
P. Bonicatto, Lagrangian representations of vector fields with special structure (2017)
Published papers
A. Arroyo-Rabasa, P. Bonicatto, and G. Del Nin, Local Poincaré constants and mean oscillation functionals for BV functions, Rev. Mat. Iberoam. (2026) to appear - arXiv: 2402.10794
P. Bonicatto, G. Del Nin, and F. Rindler, Transport of currents and geometric Rademacher-type theorems, Trans. Amer. Math. Soc. 378 (2025), p. 4011–4075 online version
P. Bonicatto, G. Ciampa, and G. Crippa, A regularity result for the Fokker-Planck equation with non-smooth drift and diffusion, Nonlinear Analysis, Theory, Methods and Applications, 254 (2025) online version
P. Bonicatto, G. Del Nin, and F. Rindler, Existence and uniqueness for the transport of currents by Lipschitz vector fields, J. Funct. Anal., 286 (2024) online version
P. Bonicatto, G. Ciampa, and G. Crippa, Weak and parabolic solutions of advection–diffusion equations with rough velocity field, J. Evol. Equ., 24 (2024) online version
A. Arroyo-Rabasa, P. Bonicatto, and G. Del Nin, Representation of the total variation as a Γ-limit of BMO-type seminorms, Indiana University Mathematics Journal, 73 (2024), p. 341–365 online version
A. Arroyo-Rabasa and P. Bonicatto, A Bourgain–Brezis–Mironescu representation for functions with bounded deformation, Calc. Var. Partial Differential Equations, 62 (2023) online version
P. Bonicatto, G. Ciampa, and G. Crippa, On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity, J. Math. Pures Appl., 167 (2022), pp. 204–224 online version
P. Bonicatto, G. Del Nin, and E. Pasqualetto, Decomposition of integral metric currents, J. Funct. Anal., 282 (2022) online version
P. Bonicatto and N. A. Gusev, On the structure of divergence-free measures in R^2, Adv. Calc. Var., 15 (2022), pp. 879–911 online version
P. Bonicatto and E. Marconi, Regularity estimates for the flow of BV autonomous divergence free vector fields in R^2, Comm. Partial Differential Equations, 46 (2021), pp. 2235–2267 online version
S. Bianchini and P. Bonicatto, Forward untangling and applications to the uniqueness problem for the continuity equation, Discrete Contin. Dyn. Syst., 41 (2021), pp. 2739–2776 online version
S. Bianchini and P. Bonicatto, A uniqueness result for the decomposition of vector fields in R^d, Invent. Math., 220 (2020), pp. 255–393 online version
P. Bonicatto, E. Pasqualetto, and T. Rajala, Indecomposable sets of finite perimeter in doubling metric measure spaces, Calc. Var. Partial Differential Equations, 59 (2020), pp. 39, Paper No. 63 online version
P. Bonicatto and N. A. Gusev, Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl., 30 (2019), pp. 511–531 online version
S. Bianchini and P. Bonicatto, Failure of the chain rule in the non steady two-dimensional setting, in Current research in nonlinear analysis, vol. 135 of Springer Optim. Appl., Springer, Cham, (2018), pp. 33–60 online version
S. Bianchini, P. Bonicatto, and N. A. Gusev, Renormalization for autonomous nearly incompressible BV vector fields in two dimensions, SIAM J. Math. Anal., 48 (2016), pp. 1–33 online version
Surveys & proceedings
P. Bonicatto, On the transport of currents, Milan Journal of Mathematics, (2024)
P. Bonicatto and N. A. Gusev, Weak superposition principle for signed measure-valued solutions of the continuity. Preprint (2021)
S. Bianchini and P. Bonicatto, Untangling of trajectories for non-smooth vector fields and Bressan’s Compactness Conjecture, in Proceedings of the 17-th Conference on Hyperbolic Problems, 2020
P. Bonicatto, On uniqueness of weak solutions to transport equation with non-smooth velocity field, in Theory, numerics and applications of hyperbolic problems. I, vol. 236 of Springer Proc. Math. Stat., Springer, Cham, (2018), pp. 191–203
S. Bianchini, P. Bonicatto, and E. Marconi, Lagrangian representations between linear transport and scalar conservation laws, in Nonlinear analysis in geometry and applied mathematics. Part 2, vol. 2 of Harv. Univ. Cent. Math. Sci. Appl. Ser. Math., Int. Press, Somerville, MA, (2018), pp. 1–22
P. Bonicatto and N. A. Gusev, Superposition principle for the continuity equation in a bounded domain, J. Phys. Conf. Ser., 990 (2018)