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

    6009 Perth

    Australia

  • 4628 Citations
  • 28 h-Index
20002019
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Research Output 2000 2019

1 Citation (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
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
19 Citations (Scopus)

1D symmetry for solutions of semilinear and quasilinear elliptic equations

Farina, A. & Valdinoci, E., 1 Feb 2011, In : Transactions of the American Mathematical Society. 363, 2, p. 579-609 31 p.

Research output: Contribution to journalArticle

Quasilinear Elliptic Equation
Semilinear Elliptic Equations
Singular Elliptic Equation
Symmetry
Degenerate Elliptic Equations
124 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
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
2 Citations (Scopus)

A comparison principle for a sobolev gradient semi-flow

Blass, T., De La Llave, R. & Valdinoci, E., 1 Jan 2011, In : Communications on Pure and Applied Analysis. 10, 1, p. 69-91 23 p.

Research output: Contribution to journalArticle

Sobolev Gradient
Sobolev spaces
Semiflow
Comparison Principle
Gradient Descent
155 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
15 Citations (Scopus)
Open Access
Weighted Sobolev Spaces
Fractional
Compact Support
Smooth function
Invariant
14 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
3 Citations (Scopus)

A fully nonlinear problem with free boundary in the plane

De Silva, D. & Valdinoci, E., 1 Dec 2010, In : Annali della Scuola Normale - Classe di Scienze. 9, 1, p. 111-132 22 p.

Research output: Contribution to journalArticle

Maximum principle
Fully Nonlinear
Bounded Solutions
Free Boundary Problem
Maximum Principle
24 Citations (Scopus)
Type Theory
Partial differential equation
Differential equation
Quasi-periodic Solutions
Elliptic PDE
8 Citations (Scopus)

A geometric inequality for stable solutions of semilinear elliptic problems in the Engel group

Pinamonti, A. & Valdinoci, E., 1 Jan 2012, In : Annales Academiae Scientiarum Fennicae Mathematica. 37, 1, p. 357-373 17 p.

Research output: Contribution to journalArticle

Open Access
Geometric Inequalities
Semilinear Elliptic Problem
Stable Solution
Mean Curvature
Test function
17 Citations (Scopus)

A geometric inequality in the Heisenberg group and its applications to stable solutions of semilinear problems

Ferrari, F. & Valdinoci, E., 1 Feb 2009, In : Mathematische Annalen. 343, 2, p. 351-370 20 p.

Research output: Contribution to journalArticle

Geometric Inequalities
Stable Solution
Heisenberg Group
Semilinear
Mean Curvature
8 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

All functions are (Locally) s-Harmonic (up to a small error)—and applications

Valdinoci, E., 2018, In : Lecture Notes in Mathematics. 2211, p. 197-214 18 p.

Research output: Contribution to journalArticle

Open Access
Fractional Laplacian
Harmonic
Similarity
18 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
7 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
11 Citations (Scopus)
Open Access
Nonlocal Equations
Identification Problem
Fractional Order
Evolution Equation
Fractional
1 Citation (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)

A nonlocal concave-convex problem with nonlocal mixed boundary data

Abdellaoui, B., Dieb, A. & Valdinoci, E., 1 May 2018, In : Communications on Pure and Applied Analysis. 17, 3, p. 1103-1120 18 p.

Research output: Contribution to journalArticle

Open Access
Dirichlet
Concave-convex Nonlinearities
Normalizing Constant
Fractional Laplacian
Neumann Condition
9 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)

A note on the construction of Hamiltonian trajectories along heteroclinic chains

Chierchia, L. & Valdinoci, E., 1 Dec 2000, In : Forum Mathematicum. 12, 2, p. 247-255 9 p.

Research output: Contribution to journalArticle

Hamiltonians
Heteroclinic Orbit
Codimension
Torus
Orbits
25 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
7 Citations (Scopus)

A one-dimensional symmetry result for a class of nonlocal semilinear equations in the plane

Hamel, F., Ros-Oton, X., Sire, Y. & Valdinoci, E., 2017, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 34, 2, p. 469-482 14 p.

Research output: Contribution to journalArticle

Open Access
Nonlocal Equations
Semilinear Equations
Symmetry
Entire Solution
Stable Solution
6 Citations (Scopus)

A pointwise gradient bound for elliptic equations on compact manifolds with nonnegative ricci curvature

Farina, A. & Valdinoci, E., 1 Aug 2011, In : Discrete and Continuous Dynamical Systems. 30, 4, p. 1139-1144 6 p.

Research output: Contribution to journalArticle

5 Citations (Scopus)
Open Access
Degenerate Problems
Gradient Estimate
Pointwise Estimates
Nonnegative Curvature
Unbounded Domain
16 Citations (Scopus)

A pointwise gradient estimate in possibly unbounded domains with nonnegative mean curvature

Farina, A. & Valdinoci, E., 1 Dec 2010, In : Advances in Mathematics. 225, 5, p. 2808-2827 20 p.

Research output: Contribution to journalArticle

Open Access
Gradient Estimate
Pointwise Estimates
Nonnegative Curvature
Unbounded Domain
Mean Curvature
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

A rigidity result for non-local semilinear equations

Farina, A. & Valdinoci, E., 2017, In : Proceedings of the Royal Society of Edinburgh Section A: Mathematics. 147, 5, p. 1009-1018 10 p.

Research output: Contribution to journalArticle

Nonlocal Equations
Semilinear Equations
Integro-differential Equation
Rigidity
Infinity
5 Citations (Scopus)
Open Access
Fractional Diffusion
Purkinje Cells
Traveling Wave
Theoretical Models
mathematical models
4 Citations (Scopus)

A symmetry result for a general class of divergence form PDEs in fibered media

Chermisi, M. & Valdinoci, E., 1 Aug 2010, In : Nonlinear Analysis, Theory, Methods and Applications. 73, 3, p. 695-703 9 p.

Research output: Contribution to journalArticle

Divergence
Symmetry
Form
Class

A symmetry result for elliptic systems in punctured domains

Biagi, S., Valdinoci, E. & Vecchi, E., 1 Sep 2019, In : Communications on Pure and Applied Analysis. 18, 5, p. 2819-2833 15 p.

Research output: Contribution to journalArticle

Open Access
Elliptic Systems
Symmetry
Boundary conditions
Hyperplane
System of equations
8 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
7 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
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
23 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
1 Citation (Scopus)
Open Access
Nonlinear analysis
Phase Transition
Phase transitions
Allen-Cahn Equation
Symmetry

A weighted gradient theory of phase transitions with a possibly singular and degenerate spatial inhomogeneity

Palatucci, G. & Valdinoci, E., 1 Mar 2012, In : Journal of Differential Equations. 252, 5, p. 3381-3402 22 p.

Research output: Contribution to journalArticle

Open Access
Inhomogeneity
Free energy
Phase Transition
Phase transitions
Gradient
28 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
2 Citations (Scopus)

Bernoulli jets and the zero mean curvature equation

Valdinoci, E., 15 Jun 2006, In : Journal of Differential Equations. 225, 2, p. 710-736 27 p.

Research output: Contribution to journalArticle

Fluid mechanics
Mean Curvature
Bernoulli
Level Set
Viscosity
99 Citations (Scopus)

Bernstein and De Giorgi type problems: New results via a geometric approach

Farina, A., Sciunzi, B. & Valdinoci, E., 1 Dec 2008, In : Annali della Scuola Normale - Classe di Scienze. 7, 4, p. 741-791 51 p.

Research output: Contribution to journalArticle

Geometric Approach
Symmetry
Singular Elliptic Equation
Degenerate Elliptic Equations
Stable Solution
24 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
38 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
10 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
11 Citations (Scopus)

Bump solutions for the mesoscopic Allen-Cahn equation in periodic media

Novaga, M. & Valdinoci, E., 1 Jan 2011, In : Calculus of Variations and Partial Differential Equations. 40, 1, p. 37-49 13 p.

Research output: Contribution to journalArticle

Allen-Cahn Equation
Periodic Media
Double-well Potential
H-function
Periodic Functions
1 Citation (Scopus)

Capillarity problems with nonlocal surface tension energies

Maggi, F. & Valdinoci, E., 2017, In : Communications in Partial Differential Equations. 42, 9, p. 1403-1446 44 p.

Research output: Contribution to journalArticle

Open Access
Capillarity
Surface Tension
Surface tension
Isoperimetric Problem
Energy Functional
7 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

Classification of irregular free boundary points for non-divergence type equations with discontinuous coefficients

Dipierro, S., Karakhanyan, A. & Valdinoci, E., 1 Dec 2018, Discrete and Continuous Dynamical Systems - Series A. 12 ed. Vol. 38. p. 6073-6090 18 p. (Discrete and Continuous Dynamical Systems- Series A).

Research output: Chapter in Book/Conference paperConference paper

Open Access
Discontinuous Coefficients
Invariance
Free Boundary
Irregular
Discontinuity
2 Citations (Scopus)
Open Access
Nonnegative Curvature
Stable Solution
Ricci Curvature
Nonlinear Boundary Conditions
Riemannian Manifold