17 citations · 46 across the 14 of their papers we have counts for
19 papers
From to : An endpoint Korn estimate
Marco Caroccia
In this short note we prove that, given a -elliptic operator and a map satisfying \( \nabla_{\mathrm{ap}}u\in L^1(Ω;…
Rigidity and functional properties of
Marco Caroccia, Nicolas Van Goethem
We provide a structural analysis of the space of functions of bounded deviatoric deformation, , which arises in models of plasticity and fluid mechanics. The mai…
Iterative blow-ups for maps with bounded -variation: a refinement, with application to and
Marco Caroccia, Nicolas Van Goethem
We refine the iterated blow-up techniques. This technique, combined with a rigidity result and a specific choice of the kernel projection in the Poincaré inequality, might be emplo…
On the emergence of almost-honeycomb structures in low-energy planar clusters
Marco Caroccia, Kenneth DeMason, Francesco Maggi
Several commonly observed physical and biological systems are arranged in shapes that closely resemble an honeycomb cluster, that is, a tessellation of the plane by regular hexagon…
On the singular planar Plateau problem
Marco Caroccia, Riccardo Scala
Given any , image of a Lipschitz curve , not necessarily injective, we provide an explicit formula for…
Isoperimetric sets and -Cheeger sets are in bijection
Marco Caroccia, Giorgio Saracco
Given an open, bounded, planar set , we consider its -Cheeger sets and its isoperimetric sets. We study the set-valued map $\mathfrak{V}:[\frac12,+\infty)\rightarrow\mathcal{…
A Compactness Theorem for functions on Poisson point clouds
Marco Caroccia
In this work we show a compactness Theorem for discrete functions on Poisson point clouds. We consider sequences with equibounded non-local -Dirichlet energy: the novelty consis…
Asymptotic behavior of the Dirichlet energy on Poisson point clouds
Andrea Braides, Marco Caroccia
We prove that quadratic pair interactions for functions defined on planar Poisson clouds and taking into account pairs of sites of distance up to a certain (large-enough) threshold…
Dimensional lower bounds for contact surfaces of Cheeger sets
Marco Caroccia, Simone Ciani
We carry on an analysis of the size of the contact surface of a Cheeger set with the boundary of its ambient space . We show that this size is strongly related to the regula…
On the Gamma convergence of functionals defined over pairs of measures and energy-measures
Marco Caroccia, Riccardo Cristoferi
A novel general framework for the study of -convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $Γ…
On the integral representation of variational functionals on
Marco Caroccia, Matteo Focardi, Nicolas Van Goethem
Following the global method for relaxation we prove an integral representation result for a large class of variational functionals naturally defined on the space of functions with…
Mumford-Shah functionals on graphs and their asymptotics
Marco Caroccia, Antonin Chambolle, Dejan Slepčev
We consider adaptations of the Mumford-Shah functional to graphs. These are based on discretizations of nonlocal approximations to the Mumford-Shah functional. Motivated by applica…
Damage-driven fracture with low-order potentials: asymptotic behavior, existence and applications
Marco Caroccia, Nicolas Van Goethem
We study the -convergence of damage to fracture energy functionals in the presence of low-order nonlinear potentials that allows us to model physical phenomena such as fluid-dri…
The Cheeger N-problem in terms of BV functions
Marco Caroccia, Samuel Littig
We reformulate the Cheeger N partition problem as a minimization among a suitable class of BV functions. This allows us to obtain a new existence proof for the Cheeger-N-problem. M…
Equilibria configurations for epitaxial crystal growth with adatoms
Marco Caroccia, Riccardo Cristoferi, Laurent Dietrich
The behavior of a surface energy , where is a set of finite perimeter and is studied. These energies have been recently c…
On the isoperimetric properties of Planar N-clusters
Marco Caroccia
This Thesis aims to highlight some isoperimetric questions involving the, so-called, -clusters. We first briefly recall the theoretical framework we are adopting. This is done i…
Cheeger -clusters
Marco Caroccia
In this paper we introduce a Cheeger-type constant defined as a minimization of a suitable functional among all the -clusters contained in an open bounded set . Here with …
A note on the stability of the Cheeger constant of -gons
Marco Caroccia, Robin Neumayer
The regular -gon provides the minimal Cheeger constant in the class of all -gons with fixed volume. This result is due to a work of Bucur and Fragalà in 2014. In this note, w…
A sharp quantitative version of Hales' isoperimetric honeycomb theorem
Marco Caroccia, Francesco Maggi
We prove a sharp quantitative version of Hales' isoperimetric honeycomb theorem by exploiting a quantitative isoperimetric inequality for polygons and an improved convergence theor…