6 papers
The Space-Time Connectivity Theorem for Normal Currents
Paolo Bonicatto, Filip Rindler, Harry Turnbull
This work establishes a Space-Time Connectivity Theorem for normal currents. In analogy with classical results of Federer and Fleming, this result allows one to witness the weak* c…
A topological characterization of indecomposable sets of finite perimeter
Paolo Bonicatto, Panu Lahti, Enrico Pasqualetto
We prove that a set of finite perimeter is indecomposable if and only if it is, up to a choice of suitable representative, connected in the 1-fine topology. This gives a topologica…
A general Frobenius' Theorem via the Transport of Currents
Paolo Bonicatto
A classical result in Differential Geometry states that the flows of two smooth vector fields commute if and only if their Lie Bracket vanishes. In this work, we extend this result…
Well-posedness of the transport of normal currents by time-dependent vector fields
Paolo Bonicatto, Giacomo Del Nin
We prove existence and uniqueness for the transport equation for currents (Geometric Transport Equation) when the driving vector field is time-dependent, Lipschitz in space and mer…
Homogenization of elasto-plastic evolutions driven by the flow of dislocations
Paolo Bonicatto, Filip Rindler
Starting from a prototypical model of elasto-plasticity in the small-strain and quasi-static setting, where the evolution of the plastic distortion is driven exclusively by the mot…
A regularity result for the Fokker-Planck equation with non-smooth drift and diffusion
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a un…