# Dr Paolo Bonicatto

## Paolo Bonicatto

Research Fellow

Office: B1.26
Phone: +44 (0)24 761 50903
Email: Paolo.Bonicatto@warwick.ac.uk

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.

Essential CV

Here is my full CV.

Selected publications

• 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 $R^2$, 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 $R^2$, 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
• 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 $R^d$, 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