1 citations · 2 across the 9 of their papers we have counts for
9 papers
-convergence of free discontinuity problems for circle-valued maps in the linear regime
Giovanni Bellettini, Roberta Marziani, Riccardo Scala
We investigate the -convergence of Ambrosio-Tortorelli type-functionals for circle valued functions, in the case of volume terms with linear growth. We show the emergence of a n…
On jump minimizing liftings for -valued maps and connections with Ambrosio-Tortorelli-type -limits
Giovanni Bellettini, Roberta Marziani, Riccardo Scala
This paper is concerned with the -limits of Ambrosio-Tortorelli-type functionals, for maps defined on an open bounded set and taking values in the unit…
Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation
Roberta Marziani, Francesco Solombrino
We analyse the -convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit i…
Line-tension limits for line singularities and application to the mixed-growth case
Sergio Conti, Adriana Garroni, Roberta Marziani
We study variational models for dislocations in three dimensions in the line-tension scaling. We present a unified approach which allows to treat energies with subquadratic growth…
-convergence and stochastic homogenisation of phase-transition functionals
Roberta Marziani
In this paper we studythe asymptotics of singularly perturbed phase-transition functionals of the form \[ F_k(u)=\frac{1}{ε_k}\int_A f_k(x,u,ε_k\nabla u)\,dx\,, \] where $u \in [0,…
Gradient damage models for heterogeneous materials
Annika Bach, Teresa Esposito, Roberta Marziani +1
In this paper we study the asymptotic behaviour of phase-field functionals of Am brosio and Tortorelli type allowing for small-scale oscillations both in the volume and in the diff…
A non-parametric Plateau problem with partial free boundary
Giovanni Bellettini, Roberta Marziani, Riccardo Scala
We consider a Plateau problem in codimension in the non-parametric setting. A Dirichlet boundary datum is given only on part of the boundary of a bounded convex do…
-convergence and stochastic homogenisation of singularly-perturbed elliptic functionals
Annika Bach, Roberta Marziani, Caterina Ida Zeppieri
We study the limit behaviour of singularly-perturbed elliptic functionals of the form \[ \mathcal F_k(u,v)=\int_A v^2\,f_k(x,\nabla u)dx+\frac{1}{\varepsilon_k}\int_A g_k(x,v,\vare…
Nonlinear three-dimensional derivation of line tension for dislocations: quadratic growth
Adriana Garroni, Roberta Marziani, Riccardo Scala
In this paper we derive a line tension model for dislocations in 3d starting from a geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as the…