23 citations · 45 across the 16 of their papers we have counts for
18 papers
Minimizers of one-dimensional regularization problems with linear and nonlinear total variation
Luca Lussardi, Marco Morandotti, Federico Stra
A study of the minimizers of one-dimensional Rudin-Osher-Fatemi-type functionals with linear or nonlinear total variation and fidelity term is undertaken. Conditions on the input d…
A variational analysis of nematic axisymmetric films: the covariant derivative case
Giulia Bevilacqua, Chiara Lonati, Luca Lussardi +1
Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi [11] and…
-convergence of discrete energies modeling self-aggregation of stochastic particles
Luca Lussardi, Anderson Melchor Hernandez, Marco Morandotti
In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the -limit of a family of discrete…
Geometric invariants of non-smooth framed curves
Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
We compare the Serret-Frenet frame with a {\em relatively parallel adapted frame} (RPAF) introduced by Bishop to parametrize -curves. Next, we derive the geometric invaria…
Elastic membranes spanning deformable boundaries
Francesco Ballarin, Giulia Bevilacqua, Luca Lussardi +1
We perform a variational analysis of an elastic membrane spanning a closed curve which may sustain bending and torsion. First, we deal with parametrized curves and linear elastic m…
Direct minimization of the Canham--Helfrich energy on generalized Gauss graphs
Anna Kubin, Luca Lussardi, Marco Morandotti
The existence of minimizers of the Canham--Helfrich functional in the setting of generalized Gauss graphs is proved. As a first step, the Canham--Helfrich functional, usually defin…
Variational analysis of inextensible elastic curves
Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange mult…
Lipschitz minimizers for a class of integral functionals under the bounded slope condition
Sebastiano Don, Luca Lussardi, Andrea Pinamonti +1
We consider the functional where is convex and and we study the minimizers in of the as…
Asymptotic analysis of a family of non-local functionals on sets
Michela Eleuteri, Luca Lussardi, Andrea Torricelli
We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first…
Existence of varifold minimizers for the multiphase Canham-Helfrich functional
Katharina Brazda, Luca Lussardi, Ulisse Stefanelli
We address the minimization of the Canham-Helfrich functional in presence of multiple phases. The problem is inspired by the modelization of heterogeneous biological membranes, whi…
On the anisotropic Kirchhoff-Plateau problem
Antonio De Rosa, Luca Lussardi
We extend to the anisotropic setting the existence of solutions for the Kirchhoff-Plateau problem and its dimensional reduction.
Soap film spanning an elastic link
Giulia Bevilacqua, Luca Lussardi, Alfredo Marzocchi
We study the equilibrium problem of a system consisting by several Kirchhoff rods linked in an arbitrary way and tied by a soap film, using techniques of the Calculus of Variations…
Stochastic homogenization of maximal monotone relations and applications
Luca Lussardi, Stefano Marini, Marco Veneroni
We study the homogenization of a stationary random maximal monotone operator on a probability space equipped with an ergodic dynamical system. The proof relies on Fitzpatrick's var…
Solution of the Kirchhoff-Plateau problem
Giulio G. Giusteri, Luca Lussardi, Eliot Fried
The Kirchhoff-Plateau problem concerns the equilibrium shapes of a system in which a flexible filament in the form of a closed loop is spanned by a liquid film, with the filament b…
Gamma convergence of a family of surface--director bending energies with small tilt
Luca Lussardi, Matthias Röger
We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in equipped with a director field. The energies strongly penalize the…
Variational analysis of a mesoscale model for bilayer membranes
Luca Lussardi, Mark A. Peletier, Matthias Röger
We present an asymptotic analysis of a mesoscale energy for bilayer membranes that has been introduced and analyzed in two space dimensions by the second and third author (Arch. Ra…
A Remark on the Anisotropic Outer Minkowski content
Antonin Chambolle, Stefano Lisini, Luca Lussardi
We study an anisotropic version of the outer Minkowski content of a closed set in Rn. In particular, we show that it exists on the same class of sets for which the classical outer…
Continuous limits of discrete perimeters
Antonin Chambolle, Alessandro Giacomini, Luca Lussardi
We consider a class of discrete convex functionals which satisfy a (generalized) coarea formula, and study their limit in the continuum.