4 citations · 7 across the 15 of their papers we have counts for
9 papers · 1 filter
Boundary rectifiability and compactness of integral currents via functions
Giacomo Del Nin
We present a new proof that an integer rectifiable current with finite mass, and whose boundary has also finite mass, is integral. We deduce the result from De Giorgi's structure t…
Turbulent Dynamos on Bounded Domains and Their Generalization to the Geometric Transport Equation
Giacomo Del Nin, Daniel Faraco, Sauli Lindberg +1
For any smooth bounded domain , we construct a divergence-free velocity field for all , and magnetic fields $B^ε\in L_t^…
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…
The square sticky disk: crystallization and Gamma-convergence to the octagonal anisotropic perimeter
Giacomo Del Nin, Lucia De Luca
We consider a variant of the sticky disk energy where distances between particles are evaluated through the sup norm in the plane. We first prove crystal…
Approximation of divergence-free vector fields vanishing on rough planar sets
Giacomo Del Nin, Bian Wu
Given any divergence-free vector field of Sobolev class in a bounded open subset , we are interested in approximating it in the norm…
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…
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…