3 papers
math.AP2026
Periodic ground states for a one-parameter family of nonlocal energies on the real line
Lucia De Luca, Giovanni Pini, Marcello Ponsiglione +1
In dimension one, we introduce a one-parameter family of nonlocal energies, including subcritical Gagliardo seminorms and Riesz functionals, acting on scalar functions whose deriva…
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 in the plane. We first prove crystal…
math.AP2024
Approximation of topological singularities through free discontinuity functionals: the critical and super-critical regimes
Vito Crismale, Lucia De Luca, Riccardo Scala
We further investigate the properties of an approach to topological singularities through free discontinuity functionals of Mumford-Shah type proposed in \cite{DLSVG}. We prove the…