Giacomo Del Nin

activity

20242026

collaborators

6 papers

math.AP2026

Boundary rectifiability and compactness of integral currents via $B V$ 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…

math.AP2026

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 $I^c ◯ \subset R^{3}$ , we construct a divergence-free velocity field $u \in L_{t}^{1} W^{1, p} (I^c ◯)$ for all $p < \infty$ , and magnetic fields $B^Îµ\in L…

math.CA2025

Marstrand's density theorem for arbitrary norms in the plane

Giacomo Del Nin, Andrea Merlo

We show that if a non-trivial measure in the plane admits, at almost every point, positive and finite $I^\pm$ -dimensional density with respect to some norm, then $I^\pm$ must be an integ…

math.AP2025

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…

math.AP2025

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 $∥ \cdot ∥_{\infty}$ in the plane. We first prove crystal…

math.AP2024

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 $W_{0}^{m, p} (I^c ◯)$ in a bounded open subset $I^c ◯ \subset R^{2}$ , we are interested in approximating it in the $W^{m, p}$ no…