82 citations · 143 across the 36 of their papers we have counts for
28 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 nonloca…
Parabolic -Riesz flows and limit cases ,
Lucia De Luca, Massimiliano Morini, Marcello Ponsiglione +1
In this paper we introduce the notion of parabolic -Riesz flow, for , extending the notion of -fractional heat flows to negative values of the parameter $s=-\fracα…
-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions
Roberto Alicandro, Lucia De Luca, Mariapia Palombaro +1
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analy…
Two slope functions minimizing fractional seminorms and applications to misfit dislocations
Lucia De Luca, Marcello Ponsiglione, Emanuele Spadaro
We consider periodic piecewise affine functions, defined on the real line, with two given slopes and prescribed length scale of the regions where the slope is negative. We prove th…
Coarse-graining of a discrete model for edge dislocations in the regular triangular lattice
Roberto Alicandro, Lucia De Luca, Giuliano Lazzaroni +2
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pai…