Lucia De Luca

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20222024

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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…

math.AP2023

$Γ$ -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…

math.AP2022

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…

Approximation of topological singularities through free discontinuity functionals: the critical and super-critical regimes

Γ-convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions

Two slope functions minimizing fractional seminorms and applications to misfit dislocations

$Γ$ -convergence analysis of the nonlinear self-energy induced by edge dislocations in semi-discrete and discrete models in two dimensions