2 citations · 3 across the 5 of their papers we have counts for
5 papers
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 crystallization result in two dimensions for a soft disc affine potential
Giacomo Del Nin, Lucia De Luca
We prove finite crystallization for particles in the plane interacting through a soft disc potential, as originally shown by C. Radin \cite{Radin_soft}. We give an alternative proo…
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…