14 citations · 58 across the 17 of their papers we have counts for
20 papers
Decomposition of functions of bounded variation in Ahlfors-regular PI spaces
Paolo Bonicatto, Panu Lahti, Enrico Pasqualetto
We prove that, on a non-compact Ahlfors-regular PI space, every function of bounded variation can be decomposed as a countable sum of monotone functions…
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…
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…
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…
Local Poincaré constants and mean oscillation functionals for functions
Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin
We introduce the concept of local Poincaré constant of a function as a tool to understand the relation between its mean oscillation and its total variation at small scales. Th…
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…
Weak and parabolic solutions of advection-diffusion equations with rough velocity field
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
We study the Cauchy problem for the advection-diffusion equation associated with a merely integrable divergence-free vector field defi…
Existence and uniqueness for the transport of currents by Lipschitz vector fields
Paolo Bonicatto, Giacomo Del Nin, Filip Rindler
This work establishes the existence and uniqueness of solutions to the initial-value problem for the geometric transport equation $$ \frac{\mathrm{d}}{\mathrm{d} t}T_t+\mathcal{L}_…
Transport of currents and geometric Rademacher-type theorems
Paolo Bonicatto, Giacomo Del Nin, Filip Rindler
The transport of many kinds of singular structures in a medium, such as vortex points/lines/sheets in fluids, dislocation loops in crystalline plastic solids, or topological singul…
Representation of the total variation as a -limit of -type seminorms
Adolfo Arroyo-Rabasa, Paolo Bonicatto, Giacomo Del Nin
We address a question raised by Ambrosio, Bourgain, Brezis, and Figalli, proving that the -limit, with respect to the topology, of a family of -type seminor…
On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
We deal with the vanishing viscosity scheme for the transport/continuity equation drifted by a divergence-free vector field $\bol…
A Bourgain-Brezis-Mironescu representation for functions with bounded deformation
Adolfo Arroyo-Rabasa, Paolo Bonicatto
We establish a non-local integral difference quotient representation for symmetric gradient semi-norms in and , which does not require the manipulation of distributi…
Decomposition of integral metric currents
Paolo Bonicatto, Giacomo Del Nin, Enrico Pasqualetto
In the setting of complete metric spaces, we prove that integral currents can be decomposed as a sum of indecomposable components. In the special case of one-dimensional integral c…
On the structure of divergence-free measures on
Paolo Bonicatto, Nikolay A. Gusev
We consider the structure of divergence-free vector measures on the plane. We show that such measures can be decomposed into measures induced by closed simple curves. More generall…
Regularity estimates for the flow of BV autonomous divergence free vector fields in
Paolo Bonicatto, Elio Marconi
We consider the regular Lagrangian flow X associated to a bounded divergence-free vector field b with bounded variation. We prove a Lusin-Lipschitz regularity result for X and we s…
Indecomposable sets of finite perimeter in doubling metric measure spaces
Paolo Bonicatto, Enrico Pasqualetto, Tapio Rajala
We study a measure-theoretic notion of connectedness for sets of finite perimeter in the setting of doubling metric measure spaces supporting a weak -Poincaré inequality. Th…
Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
Paolo Bonicatto, Nikolay A. Gusev
We consider the continuity equation , where is a measurable family of (possibily signed) Borel measur…
Renormalization for autonomous nearly incompressible BV vector fields in 2D
Stefano Bianchini, Paolo Bonicatto, Nikolay A. Gusev
Given a bounded autonomous vector field , we study the uniqueness of bounded solutions to the initial value problem for the related transport…