Total variation regularization has proven to be a valuable tool in the context of optimal
control of differential equations. This is particularly attributed to the observation that TV …

In this paper we study the stochastic homogenisation of free-discontinuity functionals.
Assuming stationarity for the random volume and surface integrands, we prove the existence …

We introduce a class of n-dimensional (possibly inhomogeneous) spin-like lattice systems
presenting modulated phases with possibly different textures. Such systems can be …

We study the limit behaviour of singularly-perturbed elliptic functionals of the form F k (u,
v)=∫ A v 2 fk (x,∇ u) dx+ 1 ε k∫ A gk (x, v, ε k∇ v) dx, where u is a vector-valued Sobolev …

We propose a new Γ-convergent discrete approximation of the Mumford–Shah functional.
The discrete functionals act on functions defined on stationary stochastic lattices and take …

We analyse integral representation and\varGamma Γ-convergence properties of functionals
defined on piecewise rigid functions, that is, functions which are piecewise affine on a …

We study, through a Γ-convergence procedure, the discrete to continuum limit of Ising-type
energies of the form F_ε(u)=-i,jc_i,j^εu_iu_j, where u is a spin variable defined on a portion …

We study the large scale equilibrium behavior of Van der Waals–Cahn–Hilliard phase
transitions in stationary ergodic media. Specifically, we are interested in free energy …

We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice
spacing tends to zero. We assume that the atoms are part of a (maybe) nonperiodic lattice …

In this paper, we study the asymptotics of singularly perturbed phase-transition functionals of
the formℱ k (u)= 1/ε k∫ A fk (𝑥, u, ε k∇ u) d𝑥, where u∈[0, 1] is a phase-field variable, ε k> …