9 citations · 28 across the 42 of their papers we have counts for
15 papers · 2 filters
Optimal embedding results for fractional Sobolev spaces
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
This paper deals with the fractional Sobolev spaces , with and . Here, we use the interpolation results in [4] to provide suitable condi…
A gentle invitation to the fractional world
Nicola Abatangelo, Serena Dipierro, Enrico Valdinoci
This book is intended as a self-contained introduction to selected topics in the fractional world, focusing particularly on aspects that arise in the study of equations driven by t…
The nonlocal Harnack inequality for antisymmetric functions: an approach via Bochner's relation and harmonic analysis
Serena Dipierro, Mateusz Kwaśnicki, Jack Thompson +1
We revisit a Harnack inequality for antisymmetric functions that has been recently established for the fractional Laplacian and we extend it to more general nonlocal elliptic opera…
On non-local almost minimal sets and an application to the non-local Massari's Problem
Serena Dipierro, Enrico Valdinoci, Riccardo Villa
We consider a fractional Plateau's problem dealing with sets with prescribed non-local mean curvature. This problem can be seen as a non-local counterpart of the classical Massari'…
A threshold for higher-order asymptotic development of genuinely nonlocal phase transition energies
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We study the higher-order asymptotic development of a nonlocal phase transition energy in bounded domains and with prescribed external boundary conditions. The energy under conside…
Comparison between solutions to the linear peridynamics model and solutions to the classical wave equation
Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena +2
In this paper, we consider an equation inspired by linear peridynamics and we establish its connection with the classical wave equation. In particular, given a horizon accoun…
Homoclinic solutions for nonlocal equations and applications to the theory of atom dislocation
Serena Dipierro, Caterina Sportelli, Enrico Valdinoci
We establish the existence of homoclinic solutions for suitable systems of nonlocal equations whose forcing term is of gradient type. The elliptic operator under consideration is t…
Global perturbative elliptic problems with critical growth in the fractional setting
Serena Dipierro, Edoardo Proietti Lippi, Enrico Valdinoci
Given , , and a bounded and integrable function which is strictly positive in an open set, we show that there exist at least two nonnegative solutions of the…
Asymptotic expansion of a nonlocal phase transition energy
Serena Dipierro, Stefania Patrizi, Enrico Valdinoci +1
We study the asymptotic behavior of the fractional Allen--Cahn energy functional in bounded domains with prescribed Dirichlet boundary conditions. When the fractional power $s \in…
A general theory for the -superposition of nonlinear fractional operators
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We consider the continuous superposition of operators of the form \[ \iint_{[0, 1]\times (1, N)} (-Δ)_p^s \,u\,dμ(s,p), \] where denotes a signed measure over the set $[0, 1]\t…
A quantitative Gidas-Ni-Nirenberg-type result for the -Laplacian via integral identities
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We prove a quantitative version of a Gidas-Ni-Nirenberg-type symmetry result involving the -Laplacian. Quantitative stability is achieved here via integral identities based on t…
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…
Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We discuss the existence theory of a nonlinear problem of nonlocal type subject to Neumann boundary conditions. Differently from the existing literature, the elliptic operator unde…
Time-fractional Allen-Cahn equations versus powers of the mean curvature
Serena Dipierro, Matteo Novaga, Enrico Valdinoci
We show by a formal asymptotic expansion that level sets of solutions of a time-fractional Allen-Cahn equation evolve by a geometric flow whose normal velocity is a positive power…
The Neumann condition for the superposition of fractional Laplacians
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke f…