9 citations · 28 across the 42 of their papers we have counts for
17 papers · 1 filter
-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…
Stability and Self-Organized Patterns in Coupled Ecohydrological--Fire Dynamics: A Model of Vegetation--Rainfall--Bushfire Interactions
Serena Dipierro, Enrico Valdinoci
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and inte…
Nonlocal free boundary minimal surfaces
Marco Badran, Serena Dipierro, Enrico Valdinoci
We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain of as the (boundaries of) critical points of the fracti…
Density estimates for a (non)local variational model with degenerate double-well potential
Serena Dipierro, Alberto Farina, Giovanni Giacomin +1
In this paper we provide density estimates for a class of functions which includes all the minimizers of the energy $\mathcal{E}_s^p(u,Ω):=(1-s)\left(\frac{1}{2}\int_Ω\int_Ω\frac{|…
Weighted nonlocal area functionals without the triangle inequality
Serena Dipierro, Enrico Valdinoci, Mary Vaughan
We consider a weighted nonlocal area functional in which the coefficients do not satisfy the triangle inequality. In the context of three phase transitions, this means that one of…
-convergence of the non-local Massari functional and applications to inhomogeneous Allen-Cahn equations
Serena Dipierro, Enrico Valdinoci, Riccardo Villa
We present several asymptotic results concerning the non-local Massari Problem for sets with prescribed mean curvature. In particular, we show that the fractional Massari functiona…
Heteroclinic connections for fractional Allen-Cahn equations with degenerate potentials
Francesco De Pas, Serena Dipierro, Mirco Piccinini +1
We investigate existence, uniqueness and asymptotic behavior of minimizers of a family of non-local energy functionals of the type $$ \frac{1}{4}\iint_{\mathbb{R}^{2n}\setminus (\m…
Nonlocal operators in divergence form and existence theory for integrable data
David Arcoya, Serena Dipierro, Edoardo Proietti Lippi +2
We present an existence and uniqueness result for weak solutions of Dirichlet boundary value problems governed by a nonlocal operator in divergence form and in the presence of a da…
Self-sustaining traveling fronts for a model related to bushfires
Serena Dipierro, Enrico Valdinoci, Glen Wheeler +1
This article investigates a mathematical model for bushfire propagation, focusing on the existence and properties of translating solutions. We obtain quantitative bounds on the env…
Maximum principles and spectral analysis for the superposition of operators of fractional order
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We consider a "superposition operator" obtained through the continuous superposition of operators of mixed fractional order, modulated by a signed Borel finite measure defined over…
Fractional De Giorgi conjecture in dimension 2 via complex-plane methods
Serena Dipierro, João Gonçalves da Silva, Giorgio Poggesi +1
We provide a new proof of the fractional version of the De Giorgi conjecture for the Allen-Cahn equation in for the full range of exponents. Our proof combines a met…
Napoleonic Constructions in the Hyperbolic Plane
Serena Dipierro, Lyle Noakes, Enrico Valdinoci
In the Euclidean setting, Napoleon's Theorem states that if one constructs an equilateral triangle on either the outside or the inside of each side of a given triangle and then con…
Bushfires and Balance: Proactive versus Reactive Policies in Prescribed Burning
Serena Dipierro, Enrico Valdinoci, Glen Wheeler +1
We introduce a new mathematical model to explore the dynamic relationship between prescribed burning and bushfire occurrence, formulated as a system of ordinary differential equati…
Density estimates for a nonlocal variational model with a degenerate double-well potential via the Sobolev inequality
Serena Dipierro, Alberto Farina, Giovanni Giacomin +1
We provide density estimates for level sets of minimizers of the energy $\frac{1}{2} \int_Ω\int_Ω \frac{|u(x)-u(y)|^p}{|x-y|^{n+sp}}dxdy+\int_Ω\int_{\mathbb{R}^n\setminusΩ} \frac{|…
Logistic diffusion equations governed by the superposition of operators of mixed fractional order
Serena Dipierro, Edoardo Proietti Lippi, Caterina Sportelli +1
We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators…