29 citations · 39 across the 11 of their papers we have counts for
15 papers
Asymptotics as of the nonlocal nonparametric Plateau problem with obstacles
Claudia Bucur, Luca Lombardini
In this paper, we introduce a functional and a geometric setting for an obstacle problem for nonlocal minimal graphs. In particular we study existence of solutions, a priori estima…
Nonlocal Micromagnetics: Compactness Criteria, Existence of Minimizers, and Brown's Fundamental Theorem
Giovanni Di Fratta, Rossella Giorgio, Luca Lombardini
This paper investigates the existence and qualitative properties of minimizers for a class of nonlocal micromagnetic energy functionals defined on bounded domains. The considered e…
Continuity of s-minimal functions
Claudia Bucur, Serena Dipierro, Luca Lombardini +1
We consider the minimization property of a Gagliardo-Slobodeckij seminorm which can be seen as the fractional counterpart of the classical problem of functions of least gradient an…
Existence results for Cahn-Hilliard type systems driven by nonlocal integrodifferential operators with singular kernels
Elisa Davoli, Chiara Gavioli, Luca Lombardini
We introduce a fractional variant of the Cahn-Hilliard equation settled in a bounded domain and with a possibly singular potential. We first focus on the case of homogeneous Dirich…
Obstructions to extension of Wasserstein distances for variable masses
Luca Lombardini, Francesco Rossi
We study the possibility of defining a distance on the whole space of measures, with the property that the distance between two measures having the same mass is the Wasserstein dis…
On nonlocal minimal graphs
Matteo Cozzi, Luca Lombardini
We develop a functional analytic approach for the study of nonlocal minimal graphs. Through this, we establish existence and uniqueness results, a priori estimates, comparison prin…
-harmonic approximation of functions of least -seminorm
Claudia Bucur, Serena Dipierro, Luca Lombardini +2
We investigate the convergence as of the minimizers of the -energy for and to those of the -energy, both in the pointwis…
Minimisers of a fractional seminorm and nonlocal minimal surfaces
Claudia Bucur, Serena Dipierro, Luca Lombardini +1
The recent literature has intensively studied two classes of nonlocal variational problems, namely the ones related to the minimisation of energy functionals that act on functions…
Minimization problems involving nonlocal functionals: nonlocal minimal surfaces and a free boundary problem
Luca Lombardini
This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the -fractional perimeter and its m…
Bernstein-Moser-type results for nonlocal minimal graphs
Matteo Cozzi, Alberto Farina, Luca Lombardini
We prove a flatness result for entire nonlocal minimal graphs having some partial derivatives bounded from either above or below. This result generalizes fractional versions of cla…
Approximation of sets of finite fractional perimeter by smooth sets and comparison of local and global -minimal surfaces
Luca Lombardini
In the first part of this paper we show that a set has locally finite -perimeter if and only if it can be approximated in an appropriate sense by smooth open sets. In the se…
The Phillip Island penguin parade (a mathematical treatment)
Serena Dipierro, Luca Lombardini, Pietro Miraglio +1
Penguins are flightless, so they are forced to walk while on land. In particular, they show rather specific behaviors in their homecoming, which are interesting to observe and to d…
Complete stickiness of nonlocal minimal surfaces for small values of the fractional parameter
Claudia Bucur, Luca Lombardini, Enrico Valdinoci
In this paper, we consider the asymptotic behavior of the fractional mean curvature when . Moreover, we deal with the behavior of -minimal surfaces when the fractional…
Fractional perimeter from a fractal perspective
Luca Lombardini
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimen…
Fractional Perimeter and Nonlocal Minimal Surfaces
Luca Lombardini
This Master's thesis presents a study of the basic properties of the s-fractional perimeter and of the regularity theory of the corresponding s-minimal sets. In particular, we give…