4 papers
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…
A crystallization result in two dimensions for a soft disc affine potential
Giacomo Del Nin, Lucia De Luca
We prove finite crystallization for particles in the plane interacting through a soft disc potential, as originally shown by C. Radin \cite{Radin_soft}. We give an alternative proo…
-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…