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

    6009 Perth

    Australia

  • 5033 Citations
  • 29 h-Index
20002023
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Research Output 2000 2019

2017
7 Citations (Scopus)
Open Access
guy wires
slabs
energy
4 Citations (Scopus)

Pohozaev identities for anisotropic integrodifferential operators

Ros-Oton, X., Serra, J. & Valdinoci, E., 2017, In : Communications in Partial Differential Equations. 42, 8, p. 1290-1321 32 p.

Research output: Contribution to journalArticle

Open Access
Pohozaev Identity
Integro-differential Operators
Integration by parts
Mathematical operators
Term

Preface

Kaiser, H. C., Knees, D., Mielke, A., Rehberg, J., Rocca, E., Thomas, M. & Valdinoci, E., 2017, In : Discrete and Continuous Dynamical Systems: Series S. 10, 4, p. i-iv 4 p.

Research output: Contribution to journalEditorial

Open Access
17 Citations (Scopus)

Regularity and Bernstein-type results for nonlocal minimal surfaces

Figalli, A. & Valdinoci, E., 28 Apr 2017, In : Journal fur die Reine und Angewandte Mathematik. 2017, 729, p. 263-273

Research output: Contribution to journalArticle

Open Access
Minimal surface
Cones
Regularity
Theorem
Nonexistence
8 Citations (Scopus)

Regularity and rigidity theorems for a class of anisotropic nonlocal operators

Farina, A. & Valdinoci, E., 1 May 2017, In : Manuscripta Mathematica. 153, 1-2, p. 53-70 18 p.

Research output: Contribution to journalArticle

Open Access
Rigidity
Regularity
Operator
Theorem
Nonlinearity
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
4 Citations (Scopus)

The effect on fisher-kpp propagation in a cylinder with fast diffusion on the boundary

Rossi, L., Tellini, A. & Valdinoci, E., 2017, In : SIAM Journal on Mathematical Analysis. 49, 6, p. 4595-4624 30 p.

Research output: Contribution to journalArticle

Open Access
Fast Diffusion
Propagation
Reaction-diffusion Equations
Strip
Diffusivity
2016
3 Citations (Scopus)

1D symmetry for semilinear PDEs from the limit interface of the solution

Farina, A. & Valdinoci, E., 2016, In : Communications in Partial Differential Equations. 41, 4, p. 665-682 18 p.

Research output: Contribution to journalArticle

Open Access
Semilinear
Symmetry
Monotone
Double-well Potential
Phase Separation
8 Citations (Scopus)
Open Access
Minimal surface
Convolution
Graph in graph theory
Euler-Lagrange Equations
Mean Curvature
4 Citations (Scopus)

Monotonicity formulae and classification results for singular, degenerate, anisotropic PDEs

Cozzi, M., Farina, A. & Valdinoci, E., 2016, In : Advances in Mathematics. 293, p. 343-381 39 p.

Research output: Contribution to journalArticle

Open Access
Monotonicity Formula
Singular Elliptic Equation
Degenerate Elliptic Equations
Anisotropic Media
Degeneracy
11 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
2 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
3 Citations (Scopus)

Relaxation times for atom dislocations in crystals

Patrizi, S. & Valdinoci, E., 2016, In : Calculus of Variations and Partial Differential Equations. 55, 3, 71.

Research output: Contribution to journalArticle

Open Access
Dislocation
Dislocations (crystals)
Relaxation Time
Relaxation time
Crystal
14 Citations (Scopus)

The Dirichlet problem for nonlocal operators with singular kernels: Convex and nonconvex domains

Ros-Oton, X. & Valdinoci, E., 22 Jan 2016, In : Advances in Mathematics. 288, p. 732-790 59 p.

Research output: Contribution to journalArticle

Open Access
Singular Kernel
Dirichlet Problem
Operator
Fractional Laplacian
Regularity of Solutions
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
8 Citations (Scopus)

Asymptotically linear problems driven by fractional Laplacian operators

Fiscella, A., Servadei, R. & Valdinoci, E., 1 Jan 2015, In : Mathematical Methods in the Applied Sciences. 38, 16, p. 3551-3563 13 p.

Research output: Contribution to journalArticle

Open Access
Fractional Laplacian
Topological Methods
Asymptotically Linear
Laplace equation
Existence of Weak Solutions
73 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
6 Citations (Scopus)

Crystal Dislocations with Different Orientations and Collisions

Patrizi, S. & Valdinoci, E., 1 Jul 2015, In : Archive for Rational Mechanics and Analysis. 217, 1, p. 231-261 31 p.

Research output: Contribution to journalArticle

Open Access
Dislocation
Dislocations (crystals)
Crystal orientation
Crystal
Collision
62 Citations (Scopus)

Density properties for fractional sobolev spaces

Fiscella, A., Servadei, R. & Valdinoci, E., 1 Jan 2015, In : Annales Academiae Scientiarum Fennicae Mathematica. 40, 1, p. 235-253 19 p.

Research output: Contribution to journalArticle

Open Access
Sobolev Spaces
Fractional
Compact Support
Variational Problem
Convolution
36 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
36 Citations (Scopus)

Fractional Laplacian equations with critical Sobolev exponent

Servadei, R. & Valdinoci, E., 12 Sep 2015, In : Revista Matematica Complutense. 28, 3, p. 655-676 22 p.

Research output: Contribution to journalArticle

Fractional Laplacian
Critical Sobolev Exponent
Fractional
Integro-differential Operators
Laplace Operator
3 Citations (Scopus)

Gevrey regularity for integro-differential operators

Albanese, G., Fiscella, A. & Valdinoci, E., 1 Jan 2015, In : Journal of Mathematical Analysis and Applications. 428, 2, p. 1225-1238 14 p.

Research output: Contribution to journalArticle

Open Access
Gevrey Regularity
Fractional Laplacian
Singular Kernel
Integro-differential Operators
Gevrey Classes
55 Citations (Scopus)

Ground states and concentration phenomena for the fractional Schrödinger equation

Moustapha Fall, M., Mahmoudi, F. & Valdinoci, E., 1 Jun 2015, In : Nonlinearity. 28, 6, p. 1937-1961 25 p.

Research output: Contribution to journalArticle

Open Access
Concentration Phenomena
Ground state
Ground State
Fractional
ground state
4 Citations (Scopus)

Homogenization and Orowan's law for anisotropic fractional operators of any order

Patrizi, S. & Valdinoci, E., 1 Jun 2015, In : Nonlinear Analysis, Theory, Methods and Applications. 119, p. 3-36 34 p.

Research output: Contribution to journalArticle

Open Access
Hamiltonians
Homogenization
Fractional
Scaling
Operator
10 Citations (Scopus)

Minimization of a fractional perimeter-Dirichlet integral functional

Caffarelli, L., Savin, O. & Valdinoci, E., 1 Jul 2015, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 32, 4, p. 901-924 24 p.

Research output: Contribution to journalArticle

Open Access
Dirichlet Integral
Perimeter
Fractional
Blow-up Analysis
Monotonicity Formula
11 Citations (Scopus)

Nonlocal quantitative isoperimetric inequalities

Di Castro, A., Novaga, M., Ruffini, B. & Valdinoci, E., 1 Nov 2015, In : Calculus of Variations and Partial Differential Equations. 54, 3, p. 2421-2464 44 p.

Research output: Contribution to journalArticle

Isoperimetric Inequality
Perimeter
Minimizer
Free energy
Isoperimetric Problem
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

Preface: Special issue on rate-independent evolutions and hysteresis modelling

Bosia, S., Eleuteri, M., Rocca, E. & Valdinoci, E., 1 Aug 2015, In : Discrete and Continuous Dynamical Systems - Series S. 8, 4, p. i

Research output: Contribution to journalEditorial

Open Access
225 Citations (Scopus)

The Brezis-Nirenberg result for the fractional laplacian

Servadei, R. & Valdinoci, E., 1 Jan 2015, In : Transactions of the American Mathematical Society. 367, 1, p. 67-102 36 p.

Research output: Contribution to journalArticle

Fractional Laplacian
Fractional
Variational techniques
Laplace equation
Integro-differential Operators
4 Citations (Scopus)

Uniqueness in weighted Lebesgue spaces for a class of fractional parabolic and elliptic equations

Punzo, F. & Valdinoci, E., 1 Jan 2015, In : Journal of Differential Equations. 258, 2, p. 555-587 33 p.

Research output: Contribution to journalArticle

Open Access
Weighted Lebesgue Spaces
Elliptic Equations
Parabolic Equation
Fractional
Uniqueness
2014
169 Citations (Scopus)

A critical Kirchhoff type problem involving a nonlocal operator

Fiscella, A. & Valdinoci, E., 1 Jan 2014, In : Nonlinear Analysis, Theory, Methods and Applications. 94, p. 156-170 15 p.

Research output: Contribution to journalArticle

Integro-differential Operators
Nonnegative Solution
Operator
Continuous Function
Fractional
27 Citations (Scopus)

A notion of nonlocal curvature

Abatangelo, N. & Valdinoci, E., 3 Jul 2014, In : Numerical Functional Analysis and Optimization. 35, 7-9, p. 793-815 23 p.

Research output: Contribution to journalArticle

Open Access
Curvature
Asymptotic Convergence
Mean Curvature
Perpendicular
Fractional
9 Citations (Scopus)

A symmetry result for the ornstein-uhlenbeck operator

Cesaroni, A., Novaga, M. & Valdinoci, E., 1 Jun 2014, In : Discrete and Continuous Dynamical Systems- Series A. 34, 6, p. 2451-2467 17 p.

Research output: Contribution to journalArticle

Open Access
Ornstein-Uhlenbeck Operator
Symmetry
Bounded Solutions
Elliptic Equations
Monotone
29 Citations (Scopus)

A Widder's Type Theorem for the Heat Equation with Nonlocal Diffusion

Barrios, B., Peral, I., Soria, F. & Valdinoci, E., 1 Jan 2014, In : Archive for Rational Mechanics and Analysis. 213, 2, p. 629-650 22 p.

Research output: Contribution to journalArticle

Open Access
Nonlocal Diffusion
Heat Equation
Theorem
Nonnegative Solution
Strong Solution
42 Citations (Scopus)

Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces

Barrios, B., Figalli, A. & Valdinoci, E., 1 Jan 2014, In : Annali della Scuola normale superiore di Pisa - Classe di scienze. 13, 3, p. 609-639 31 p.

Research output: Contribution to journalArticle

Open Access
Integro-differential Operators
Regularity Theory
Integrodifferential equations
Minimal surface
Integro-differential Equation
33 Citations (Scopus)

Density estimates for a variational model driven by the Gagliardo norm

Savin, O. & Valdinoci, E., 1 Jan 2014, In : Journal des Mathematiques Pures et Appliquees. 101, 1, p. 1-26 26 p.

Research output: Contribution to journalArticle

Open Access
Variational Model
Density Estimates
Norm
Minimal surface
Level Set
15 Citations (Scopus)

Gradient Bounds and Rigidity Results for Singular, Degenerate, Anisotropic Partial Differential Equations

Cozzi, M., Farina, A. & Valdinoci, E., Oct 2014, In : Communications in Mathematical Physics. 331, 1, p. 189-214 26 p.

Research output: Contribution to journalArticle

Open Access
Anisotropic Media
Degenerate Equations
Quasilinear Equations
anisotropic media
Energy Functional
10 Citations (Scopus)

Gradient bounds for anisotropic partial differential equations

Farina, A. & Valdinoci, E., 1 Mar 2014, In : Calculus of Variations and Partial Differential Equations. 49, 3-4, p. 923-936 14 p.

Research output: Contribution to journalArticle

Rigidity
Partial differential equations
Partial differential equation
Gradient
Energy
125 Citations (Scopus)

On the spectrum of two different fractional operators

Servadei, R. & Valdinoci, E., 1 Jan 2014, In : Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 144, 4, p. 831-855 25 p.

Research output: Contribution to journalArticle

Fractional
Operator
Normalizing Constant
Fractional Laplacian
Laplace Operator
16 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
35 Citations (Scopus)

Uniqueness and Nondegeneracy of Positive Solutions of (-Δ)su + u = up in ℝN when s is Close to 1

Fall, M. M. & Valdinoci, E., Jul 2014, In : Communications in Mathematical Physics. 329, 1, p. 383-404 22 p.

Research output: Contribution to journalArticle

Open Access
Nondegeneracy
uniqueness
Positive Solution
Uniqueness
Minimizer
65 Citations (Scopus)

Weak and viscosity solutions of the fractional laplace equation

Servadei, R. & Valdinoci, E., 1 Jan 2014, In : Publicacions Matematiques. 58, 1, p. 133-154 22 p.

Research output: Contribution to journalArticle

Open Access
Viscosity Solutions
Laplace's equation
Fractional Laplacian
Weak Solution
Fractional
2013
129 Citations (Scopus)

A brezis-nirenberg result for non-local critical equations in low dimension

Servadei, R. & Valdinoci, E., 1 Nov 2013, In : Communications on Pure and Applied Analysis. 12, 6, p. 2445-2464 20 p.

Research output: Contribution to journalArticle

Open Access
Fractional
Critical Sobolev Exponent
Subset
Laplace Operator
Nontrivial Solution
18 Citations (Scopus)

A Fractional Framework for Perimeters and Phase Transitions

Valdinoci, E., 22 Mar 2013, In : Milan Journal of Mathematics. 81, 1, p. 1-23 23 p.

Research output: Contribution to journalArticle

Fractional Laplacian
Phase Coexistence
Diffusion Model
Perimeter
Fractional
9 Citations (Scopus)

A lewy-stampacchia estimate for variational inequalities in the heisenberg group

Pinamonti, A. & Valdinoci, E., 1 Dec 2013, In : Rendiconti dell'Istituto di Matematica dell'Universita di Trieste. 45, 1, p. 23-46 24 p.

Research output: Contribution to journalArticle

Open Access
Heisenberg Group
Variational Inequalities
Obstacle Problem
Operator
Estimate
1 Citation (Scopus)

A priori bounds for solutions of a nonlocal evolution PDE

Caffarelli, L. & Valdinoci, E., 1 Jan 2013, Analysis and Numerics of Partial Differential Equations. Brezzi, F., Franzone, P. C., Gianazzi, U. & Gilardi, G. (eds.). Italy: Springer International Publishing AG, p. 141-163 23 p. (Springer INdAM Series; vol. 4).

Research output: Chapter in Book/Conference paperChapter

Fractional Laplacian
A Priori Bounds
Interval
Operator
28 Citations (Scopus)

A resonance problem for non-local elliptic operators

Fiscella, A., Servadei, R. & Valdinoci, E., 22 Oct 2013, In : Zeitschrift fur Analysis und ihre Anwendung. 32, 4, p. 411-431 21 p.

Research output: Contribution to journalArticle

Resonance Problem
Integro-differential Operators
Elliptic Operator
Existence Theorem
Saddle Point Theorem
26 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