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)