9 citations · 28 across the 42 of their papers we have counts for
56 papers
Solutions of the space-fractional heat equation with polynomial growth: Liouville theorems and Schauder estimates
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci +1
With the aim of extending to parabolic equations the framework developed by the first three authors in [Dipierro, Savin, and Valdinoci, Rev. Mat. Iberoam. (2019)], we introduce a n…
Active Approach to Fast Quantum State Preparation and Reset in Atomic Arrays
Ya-Tang Yu, Wei-Hsuan Chung, Tian-Shu Gou +2
Rapid preparation of a target quantum state and reset to the many-body ground state are essential for quantum information processing. Here, we investigate both processes in a waveg…
Kernel representations of fractional gradient bilinear forms. Part II. Variable coefficients
Serena Dipierro, Caterina Sportelli, Enrico Valdinoci
This paper investigates the existence and properties of interaction kernels representing nonlocal energies associated with the Riesz fractional gradient and variable, uniformly ell…
Kernel representations of fractional gradient bilinear forms. Part I. Constant coefficients
Serena Dipierro, Caterina Sportelli, Enrico Valdinoci
We study the representation of bilinear forms associated with Riesz fractional gradients by symmetric integral kernels. Motivated by [SS18, Open Problem 1.10], we give a complete d…
On the Weyl tube formula for nonlocal perimeters
Serena Dipierro, Jack Thompson, Enrico Valdinoci
We study the asymptotic behaviour of the nonlocal perimeter of tubular neighbourhoods. For a closed submanifold of Euclidean space, we show that a suitable rescaling of t…
Boundedness of Solutions to Nonlocal Systems
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
Under mild mass or energy assumptions, we prove uniform bounds for all distributional solutions of a multi-dimensional system of nonlocal semilinear equations. The setti…
Dissolution and nucleation of jump discontinuities for one-dimensional periodic peridynamic waves
Giuseppe Maria Coclite, Serena Dipierro, Francesco Maddalena +2
We analyze solutions to a one-dimensional periodic linear model for peridynamic waves, focusing on the setting where the natural energy space allows for spatial discontinuities. Ex…
Asymptotics of nonlocal nonlinear Robin energies
Serena Dipierro, Giuseppe Spadaro, Enrico Valdinoci
We study the free minimization problem for a nonlinear, nonlocal functional associated with Robin-type nonlocal exterior conditions depending on a positive parameter . We prove…
A fractional critical problem in the halfspace with Neumann conditions
Azahara DelaTorre, Azahara DelaTorre Pedraza, Serena Dipierro +2
Given and , we construct nontrivial solutions of the problem \begin{equation*} \begin{cases} (-Δ)^s u=u^{2^*_s-1} &{\mbox{ in }}\mathbb{R}^n_+,\\ {\mathcal{N}}_s…
A free boundary analysis of tumor invasion driven by angiogenesis
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We discuss a free boundary model for tumor invasion that describes a cloud of cells that diffuse and, at the same time, are drifted along the vector field of the chemotactic direct…
A free boundary problem driven by boundary distance in the coincidence set
Amal Alphonse, Marcelo Bongarti, Enrico Valdinoci
We study a free boundary problem of minimising a functional containing a non-local term rewarding depth into the zero phase: for on a bounded, open set $Ω\subset\mat…
A logistic equation with non-local operators of order near zero
Luigi Appolloni, Serena Dipierro, Enrico Valdinoci
In this paper we study an equation driven by a non-local operator of order "near zero" with mixed Dirichlet-Neumann boundary conditions, modelling a biological system consisting of…
Nonlocal minimal surfaces are generically unique, and smooth in one extra dimension
Serena Dipierro, Xavier Fernández-Real, Enrico Valdinoci
We study the fractional Plateau problem for -minimal sets with prescribed exterior datum. For fixed exterior data, minimizers need not be unique, and singularities may occur bey…
Wildfire in a Narrow Gully: A Geometric Reduction Approach
Lorenzo De Gaspari, Serena Dipierro, Enrico Valdinoci
We consider a bushfire model in a gully. The biological scenario under consideration involves flammable fuel (trees, leaves, etc.) concentrated within the gully, surrounded by rock…
Long-range phase coexistence models with degenerate potentials
Francesco De Pas, Serena Dipierro, Enrico Valdinoci
This survey offers an overview of recent advances in nonlocal phase transition problems, modeled by Ginzburg--Landau type energies of the form \[ \frac{1}{4}\iint_{\R^{2n}\setminus…
Fredholm alternative for a general class of nonlocal operators
Francesco De Pas, Serena Dipierro, Enrico Valdinoci
We develop a Fredholm alternative for a fractional elliptic operator~ of mixed order built on the notion of fractional gradient. This operator constitutes the nonlocal…
Optimal decay of heteroclinic solutions of the fractional Allen-Cahn equation with a degenerate potential
Francesco De Pas, Serena Dipierro, Enrico Valdinoci
We refine the asymptotic estimates for minimizers of a class of nonlocal energy functionals of the form \[ \frac{1}{4} \iint_{\R^{2n} \setminus (\R^n \setminus Ω)^2} \snr{u(x) - u(…
Reconstructing double-well potentials from transition layers in long-range phase coexistence models
Serena Dipierro, Francesco De Pas, Enrico Valdinoci
In models of phase coexistence, the precise form of the double-well potential is of central importance, yet it cannot be derived from first principles. In this paper, we investigat…
Regularity of the trace of nonlocal minimal graphs
Serena Dipierro, Ovidiu Savin, Enrico Valdinoci
We prove that the trace of nonlocal minimal graphs at points of stickiness is of class~. As a result, we show that boundary continuity implies boundary differentiability f…
Non-local planelike minimizers and -convergence of periodic energies to a local anisotropic perimeter
Serena Dipierro, Matteo Novaga, Enrico Valdinoci +1
We investigate a homogenization problem related to a non-local interface energy with a periodic forcing term. We show the existence of planelike minimizers for such energy. Moreove…
On a Sobolev critical problem for the superposition of a local and nonlocal operator with the "wrong sign''
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. The main novelty is that we consider a mixed op…
-convergence for higher order nonlocal phase transitions
Hardy Chan, Serena Dipierro, Mattia Freguglia +2
For every , we study the asymptotic behavior of the -rescaled sum of the -fractional Allen-Cahn energy and the squared -norm of its first variation…
The Neumann problem for the fractional Laplacian: optimal regularity via the Mellin transform
Serena Dipierro, Xavier Ros-Oton, Enrico Valdinoci +1
We establish the optimal regularity of solutions to the Neumann problem for the fractional Laplacian, in , with the external condition in .…
On a class of (non)local superposition operators of arbitrary order
Serena Dipierro, Sven Jarohs, Enrico Valdinoci
In this paper we introduce a very general setting dealing with the superposition of operators of any positive order and provide a systematic study of them. We also provide examples…