• The University of Western Australia (M019), 35 Stirling Highway,

    6009 Perth

    Australia

  • 456 Citations
  • 12 h-Index
20112021
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Research Output 2013 2019

  • 456 Citations
  • 12 h-Index
  • 47 Article
  • 1 Conference paper
  • 1 Editorial
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Article
2019
3 Citations (Scopus)

Decay estimates for evolutionary equations with fractional time-diffusion

Dipierro, S., Valdinoci, E. & Vespri, V., 1 Jun 2019, In : Journal of Evolution Equations. 19, 2, p. 435-462 28 p.

Research output: Contribution to journalArticle

Decay Estimates
Fractional
Nonlocal Diffusion
Nonlocal Equations
Diffusion equation
1 Citation (Scopus)

Definition of fractional Laplacian for functions with polynomial growth

Dipierro, S., Savin, O. & Valdinoci, E., 1 Jan 2019, In : Revista Matematica Iberoamericana. 35, 4, p. 1079-1122 44 p.

Research output: Contribution to journalArticle

Fractional Laplacian
Polynomial Growth
Schauder Estimates
Infinity
Seminorm
44 Downloads (Pure)

Heteroclinic connections for nonlocal equations

Dipierro, S., Patrizi, S. & Valdinoci, E., 26 Nov 2019, In : Mathematical Models and Methods in Applied Sciences. 1950055.

Research output: Contribution to journalArticle

File
Heteroclinic Connection
Nonlocal Equations
Integrodifferential equations
Dislocations (crystals)
Orbits

Limit behaviour of a singular perturbation problem for the Biharmonic operator

Dipierro, S., Karakhanyan, A. L. & Valdinoci, E., 25 Jul 2019, In : Applied Mathematics and Optimization. p. 1-35

Research output: Contribution to journalArticle

Biharmonic Operator
Limit Behavior
Singular Perturbation Problems
Monotonicity Formula
Biharmonic

Minimizers of the p-oscillation functional

Cesaroni, A., Dipierro, S., Novaga, M. & Valdinoci, E., Jun 2019, In : Discrete and Continuous Dynamical Systems- Series A. 39, 12, p. 6785-6799 15 p.

Research output: Contribution to journalArticle

Minimizer
Oscillation
Compact Perturbation
Total Variation
Dirichlet Problem
3 Citations (Scopus)

On stationary fractional mean field games

Cesaroni, A., Cirant, M., Dipierro, S., Novaga, M. & Valdinoci, E., Feb 2019, In : Journal des Mathematiques Pures et Appliquees. 122, p. 1-22 22 p.

Research output: Contribution to journalArticle

Hamiltonians
Mean Field
Fractional
Game
Mathematical operators

Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions

Abatangelo, N., Dipierro, S., Fall, M. M., Jarohs, S. & Saldaña, A., 1 Mar 2019, In : Discrete and Continuous Dynamical Systems- Series A. 39, 3, p. 1205-1235 31 p.

Research output: Contribution to journalArticle

Open Access
Decay of Solutions
Half-space
Dirichlet Boundary Conditions
Boundary value problems
Dirichlet
2 Citations (Scopus)

Rigidity results in diffusion Markov triples

Dipierro, S., Pinamonti, A. & Valdinoci, E., Feb 2019, In : Journal of Functional Analysis. 276, 3, p. 785-814

Research output: Contribution to journalArticle

Open Access
Stable Solution
Rigidity
Semilinear Equations
Topological space
Linear Operator
2 Citations (Scopus)

Wellposedness of a nonlinear peridynamic model

Coclite, G. M., Dipierro, S., Maddalena, F. & Valdinoci, E., Jan 2019, In : Nonlinearity. 32, 1, p. 1-21 21 p.

Research output: Contribution to journalArticle

2018
2 Citations (Scopus)

(Non)local and (non)linear free boundary problems

Dipierro, S. & Valdinoci, E., 2018, In : DISCRETE & CONTINUOUS DYNAMICAL SYSTEMS. SERIES A. 11, 3, p. 465-476 12 p.

Research output: Contribution to journalArticle

Open Access
Free Boundary Problem
Invariance
Electron energy levels
Superposition
Energy

A new discrete monotonicity formula with application to a two-phase free boundary problem in dimension two

Dipierro, S. & Karakhanyan, A. L., 3 Jul 2018, In : Communications in Partial Differential Equations. 43, 7, p. 1073-1101 29 p.

Research output: Contribution to journalArticle

Open Access
Monotonicity Formula
Free Boundary Problem
Two Dimensions
Free Boundary
Minimizer
9 Citations (Scopus)
Open Access
Fractional Diffusion
Purkinje Cells
Traveling Wave
Theoretical Models
mathematical models
3 Citations (Scopus)
Open Access
Nonlinear analysis
Phase Transition
Phase transitions
Allen-Cahn Equation
Symmetry
5 Citations (Scopus)
Open Access
Nonnegative Curvature
Stable Solution
Ricci Curvature
Nonlinear Boundary Conditions
Riemannian Manifold
2 Citations (Scopus)

Fattening and nonfattening phenomena for planar nonlocal curvature flows

Cesaroni, A., Dipierro, S., Novaga, M. & Valdinoci, E., 11 Dec 2018, In : Mathematische Annalen.

Research output: Contribution to journalArticle

Curvature Flow
Curvature
Perimeter
kernel
Tangent line
7 Citations (Scopus)

Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Dipierro, S., Savin, O. & Valdinoci, E., 11 Jun 2018, In : Journal of Geometric Analysis. p. 1-28 28 p.

Research output: Contribution to journalArticle

Open Access
Nonlocal Equations
Local Approximation
Arbitrary
Linear equation
Operator
2 Citations (Scopus)

Minimizers for nonlocal perimeters of Minkowski type

Cesaroni, A., Dipierro, S., Novaga, M. & Valdinoci, E., 1 Apr 2018, In : Calculus of Variations and Partial Differential Equations. 57, 2, 64.

Research output: Contribution to journalArticle

Open Access
Perimeter
White noise
Minimizer
Rigidity
Concretes
1 Citation (Scopus)
Open Access
Geometric Flows
Mean Curvature Flow
Scale Invariance
Curve
Traveling Wave

The Phillip island penguin parade (A mathematical treatment)

Dipierro, S., Lombardini, L., Miraglio, P. & Valdinoci, E., 1 Jul 2018, In : Anziam Journal. 60, 1, p. 27-54 28 p.

Research output: Contribution to journalArticle

Walk
Ordinary differential equation
Existence and Uniqueness
Model
Numerical Simulation
2017
2 Citations (Scopus)

A class of unstable free boundary problems

Dipierro, S., Karakhanyan, A. & Valdinoci, E., 2017, In : Analysis and PDE. 10, 6, p. 1317-1359 43 p.

Research output: Contribution to journalArticle

Open Access
Free Boundary Problem
Perimeter
Free Boundary
Unstable
Energy Functional
26 Citations (Scopus)

All functions are locally s-harmonic up to a small error

Dipierro, S., Savin, O. & Valdinoci, E., 2017, In : Journal of the European Mathematical Society. 19, 4, p. 957-966 10 p.

Research output: Contribution to journalArticle

Open Access
Harmonic functions
Harmonic Functions
Harmonic
Compact Set
Rigidity
10 Citations (Scopus)

A logistic equation with nonlocal interactions

Caffarelli, L., Dipierro, S. & Valdinoci, E., 2017, In : Kinetic and Related Models. 10, 1, p. 141-170 30 p.

Research output: Contribution to journalArticle

Open Access
Nonlocal Interactions
Logistic Equation
Logistics
Resources
Process Modeling
2 Citations (Scopus)

A nonlinear free boundary problem with a self-driven Bernoulli condition

Dipierro, S., Karakhanyan, A. & Valdinoci, E., 2017, In : Journal of Functional Analysis. 273, 11, p. 3549-3615 67 p.

Research output: Contribution to journalArticle

Open Access
Free Boundary Problem
Minimizer
Bernoulli
Free Boundary
Blow-up
1 Citation (Scopus)

Asymptotic Expansions of the Contact Angle in Nonlocal Capillarity Problems

Dipierro, S., Maggi, F. & Valdinoci, E., 2017, In : Journal of Nonlinear Science. 27, 5, p. 1531-1550 20 p.

Research output: Contribution to journalArticle

Open Access
Capillarity
Contact Angle
Contact angle
Asymptotic Expansion
Fractional
25 Citations (Scopus)

Bifurcation results for a fractional elliptic equation with critical exponent in Rn

Dipierro, S., Medina, M., Peral, I. & Valdinoci, E., 1 May 2017, In : Manuscripta Mathematica. 153, 1-2, p. 183-230 48 p.

Research output: Contribution to journalArticle

Open Access
Elliptic Equations
Critical Exponents
Fractional
Bifurcation
Elliptic Regularity
9 Citations (Scopus)

Boggio’s formula for fractional polyharmonic Dirichlet problems

Dipierro, S. & Grunau, H. C., Aug 2017, In : Annali di Matematica Pura ed Applicata. 196, 4, p. 1327-1344 18 p.

Research output: Contribution to journalArticle

Dirichlet Problem
Fractional
Ball
Integer
Formulation
13 Citations (Scopus)

Boundary behavior of nonlocal minimal surfaces

Dipierro, S., Savin, O. & Valdinoci, E., 2017, In : Journal of Functional Analysis. 272, 5, p. 1791-1851 61 p.

Research output: Contribution to journalArticle

Open Access
Boundary Behavior
Minimal surface
Ball
Perturbation
Line
9 Citations (Scopus)

Chaotic Orbits for Systems of Nonlocal Equations

Dipierro, S., Patrizi, S. & Valdinoci, E., 1 Jan 2017, In : Communications in Mathematical Physics. 349, 2, p. 583-626 44 p.

Research output: Contribution to journalArticle

Open Access
Multibump Solutions
Integer Points
Nonlocal Equations
Symbolic Dynamics
Periodic Potential
3 Citations (Scopus)
Open Access
Free Boundary Problem
Fractional
Perimeter
Free Boundary
Minimizer
1 Citation (Scopus)

New Trends in Free Boundary Problems

Dipierro, S., Karakhanyan, A. & Valdinoci, E., 2017, In : Advanced Nonlinear Studies. 17, 2, p. 319-332 14 p.

Research output: Contribution to journalArticle

Open Access
free boundaries
Free Boundary Problem
trends
interfacial energy
Energy
43 Citations (Scopus)

Nonlocal problems with Neumann boundary conditions

Dipierro, S., Ros-Oton, X. & Valdinoci, E., 2017, In : Revista Matematica Iberoamericana. 33, 2, p. 377-416 40 p.

Research output: Contribution to journalArticle

Open Access
Neumann Condition
Nonlocal Problems
Neumann Boundary Conditions
Fractional Laplacian
Nonlocal Conditions
12 Citations (Scopus)

On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results

Dipierro, S., Soave, N. & Valdinoci, E., Dec 2017, In : Mathematische Annalen. 369, 3-4, p. 1283–1326 44 p.

Research output: Contribution to journalArticle

Open Access
Elliptic Equations
Rigidity
Lipschitz
Monotonicity
Fractional
5 Citations (Scopus)

Planelike Interfaces in Long-Range Ising Models and Connections with Nonlocal Minimal Surfaces

Cozzi, M., Dipierro, S. & Valdinoci, E., 2017, In : Journal of Statistical Physics. 167, 6, p. 1401-1451 51 p.

Research output: Contribution to journalArticle

Open Access
minimal surfaces
Minimal surface
Ising model
Ising Model
hyperplanes
1 Citation (Scopus)

Rigidity of critical points for a nonlocal Ohta-Kawasaki energy

Dipierro, S., Novaga, M. & Valdinoci, E., 2017, In : Nonlinearity. 30, 4, p. 1523-1535 13 p.

Research output: Contribution to journalArticle

Open Access
rigidity
Rigidity
Free energy
Critical point
critical point
2016
10 Citations (Scopus)
Open Access
Minimal surface
Convolution
Graph in graph theory
Euler-Lagrange Equations
Mean Curvature
12 Citations (Scopus)

Nonlocal Delaunay surfaces

Dávila, J., Del Pino, M., Dipierro, S. & Valdinoci, E., 2016, In : Nonlinear Analysis, Theory, Methods and Applications. 137, p. 357-380 24 p.

Research output: Contribution to journalArticle

Open Access
Delaunay
Perimeter
Codimension
Ball
Tend

Nonlocal phase transitions: Rigidity results and anisotropic geometry

Dipierro, S., Serra, J. & Valdinoci, E., 2016, In : Rendiconti del Seminario Matematico. 74, 3-4, p. 135-149 15 p.

Research output: Contribution to journalArticle

Open Access
Rigidity
Phase Transition
Series
Integro-differential Operators
Minimal Solution
3 Citations (Scopus)

Nonlocal phase transitions in homogeneous and periodic media

Cozzi, M., Dipierro, S. & Valdinoci, E., 5 Nov 2016, In : Journal of Fixed Point Theory and Applications. p. 1-19 19 p.

Research output: Contribution to journalArticle

Open Access
Periodic Media
Inhomogeneous Media
Phase Transition
Phase transitions
Potential energy
37 Citations (Scopus)
Qualitative Properties
Positive Solution
Moving Plane Method
Nonlocal Problems
Comparison Result
1 Citation (Scopus)

Some monotonicity results for general systems of nonlinear elliptic PDEs

Brasseur, J. & Dipierro, S., 2016, In : Journal of Differential Equations. 261, 5, p. 2854-2880

Research output: Contribution to journalArticle

Nonlinear Elliptic PDE
Monotonicity
Stable Solution
Energy Functional
Rigidity
2015
16 Citations (Scopus)
Open Access
Weighted Sobolev Spaces
Fractional
Compact Support
Smooth function
Invariant
10 Citations (Scopus)

A nonlocal free boundary problem

Dipierro, S., Savin, O. & Valdinoci, E., 1 Jan 2015, In : SIAM Journal on Mathematical Analysis. 47, 6, p. 4559-4605 47 p.

Research output: Contribution to journalArticle

Open Access
Free Boundary Problem
Perimeter
Minimization Problem
Dirichlet
Bounded Domain
74 Citations (Scopus)

Concentration phenomena for the nonlocal Schrödinger equation with Dirichlet datum

Dávila, J., Del Pino, M., Dipierro, S. & Valdinoci, E., 1 Jan 2015, In : Analysis and PDE. 8, 5, p. 1165-1235 71 p.

Research output: Contribution to journalArticle

Open Access
Concentration Phenomena
Nonlocal Equations
Green's function
Ground state
Dirichlet
38 Citations (Scopus)

Dislocation Dynamics in Crystals: A Macroscopic Theory in a Fractional Laplace Setting

Dipierro, S., Palatucci, G. & Valdinoci, E., 1 Jan 2015, In : Communications in Mathematical Physics. 333, 2, p. 1061-1105 45 p.

Research output: Contribution to journalArticle

Dislocation Dynamics
Dislocation
Laplace
Fractional
Crystal
5 Citations (Scopus)

On a fractional harmonic replacement

Dipierro, S. & Valdinoci, E., 1 Aug 2015, In : Discrete and Continuous Dynamical Systems- Series A. 35, 8, p. 3377-3392 16 p.

Research output: Contribution to journalArticle

Open Access
Replacement
Fractional
Harmonic
Boundary conditions
Energy
2014
19 Citations (Scopus)

Strongly Nonlocal Dislocation Dynamics in Crystals

Dipierro, S., Figalli, A. & Valdinoci, E., 1 Jan 2014, In : Communications in Partial Differential Equations. 39, 12, p. 2351-2387 37 p.

Research output: Contribution to journalArticle

Open Access
Dislocation Dynamics
Dislocation
Dislocations (crystals)
Crystal
Crystals
2013
27 Citations (Scopus)

Asymptotics of the s-perimeter as s ↘ 0

Dipierro, S., Figalli, A., Palatucci, G. & Valdinoci, E., 1 Jul 2013, In : Discrete and Continuous Dynamical Systems- Series A. 33, 7, p. 2777-2790 14 p.

Research output: Contribution to journalArticle

Perimeter
Lebesgue Measure
Asymptotic Behavior
Necessary Conditions
Formulation