5 papers · 1 filter
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…
Flat flows of periodic Lipschitz subgraphs for generalized nonlocal perimeters
Lucia De Luca, Antonia Diana, Marcello Ponsiglione
We prove the existence and the 1/2-Hölder continuity in time of flat flows for periodic Lipschitz subgraphs, whose evolution is governed by the gradient flow of generalized nonloc…
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 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…
Semi-discrete modeling of systems of wedge disclinations and edge dislocations via the Airy stress function method
Pierluigi Cesana, Lucia De Luca, Marco Morandotti
We present a variational theory for lattice defects of rotational and translational type. We focus on finite systems of planar wedge disclinations, disclination dipoles, and edge d…