I currently work as a Research Fellow in the group led by Filip Rindler under the ERC project SINGULARITY – Singularities and Compactness in Nonlinear PDEs.
My research interests lie mostly in Partial Differential Equations, Geometric Measure Theory and, more recently, in some aspects of the Calculus of Variations.
- 2017 - 2020: Wissenschaftlicher Mitarbeiter (Post-Doc), University of Basel (Switzerland). I worked in the group of Gianluca Crippa under the ERC project FLIRT – Fluid Flows and Irregular Transport.
- 2014 - 2017: PhD student at SISSA, under the supervision of Stefano Bianchini.
- A. Arroyo-Rabasa, P. Bonicatto and G. Del Nin, Representation of the total variation as a
Γ-limit of BMO-type seminorms, arXiv:2112.03832
- P. Bonicatto, G. Ciampa and G. Crippa, Advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity, arXiv:2107.03659
- A. Arroyo-Rabasa and P. Bonicatto, A Bourgain-Brezis-Mironescu representation for functions with bounded deformation, arXiv:2106.06954
- P. Bonicatto, G. Del Nin and E. Pasqualetto, Decomposition of integral metric currents, to appear in J. Funct. Anal (2022) arXiv:2104.07593
- P. Bonicatto and N. A. Gusev, On the structure of divergence-free measures in , to appear in Adv. Calc. Var. (2021) arXiv:1912.10936
- P. Bonicatto and E. Marconi, Regularity estimates for the flow of BV autonomous divergence-free vector fields in , 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
- 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
- S. Bianchini and P. Bonicatto, A uniqueness result for the decomposition of vector fields in , Invent. Math., 220 (2020), pp. 255-393 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