Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Lombardini, Luca"'
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 and which is related to the minimization of the nonlocal perimeter funct
Externí odkaz:
http://arxiv.org/abs/2407.20079
Publikováno v:
Nonlinear Analysis, Theory, Methods and Applications, 248 (2024), 113623
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 Dirichlet boundary conditions, and show how to prove the existence and uniqu
Externí odkaz:
http://arxiv.org/abs/2401.15738
Autor:
Lombardini, Luca, Rossi, Francesco
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 distance, up to a scaling factor. We prove that, under very weak and natu
Externí odkaz:
http://arxiv.org/abs/2112.04763
Autor:
Cozzi, Matteo, Lombardini, Luca
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 principles, rearrangement inequalities, and the equivalence of several not
Externí odkaz:
http://arxiv.org/abs/2010.16206
We investigate the convergence as $p\searrow1$ of the minimizers of the $W^{s,p}$-energy for $s\in(0,1)$ and $p\in(1,\infty)$ to those of the $W^{s,1}$-energy, both in the pointwise sense and by means of $\Gamma$-convergence. We also address the conv
Externí odkaz:
http://arxiv.org/abs/2009.14659
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 in suitable Sobolev-Gagliardo spaces, and the ones related to the mini
Externí odkaz:
http://arxiv.org/abs/2002.06313
Autor:
Lombardini, Luca
This doctoral thesis is devoted to the analysis of some minimization problems that involve nonlocal functionals. We are mainly concerned with the $s$-fractional perimeter and its minimizers, the $s$-minimal sets. We investigate the behavior of sets h
Externí odkaz:
http://arxiv.org/abs/1811.09746
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 classical theorems due to Bernstein and Moser. Our arguments rely on a ge
Externí odkaz:
http://arxiv.org/abs/1807.05774
Publikováno v:
Annales de l'Institut Henri Poincar\'e C, Analyse non lin\'eaire, 2018
In this paper, we consider the asymptotic behavior of the fractional mean curvature when $s\to 0^+$. Moreover, we deal with the behavior of $s$-minimal surfaces when the fractional parameter $s\in(0,1)$ is small, in a bounded and connected open set w
Externí odkaz:
http://arxiv.org/abs/1612.08295
Autor:
Lombardini, Luca
In the first part of this paper we show that a set $E$ has locally finite $s$-perimeter if and only if it can be approximated in an appropriate sense by smooth open sets. In the second part we prove some elementary properties of local and global $s$-
Externí odkaz:
http://arxiv.org/abs/1612.08237