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

    6009 Perth

    Australia

  • 5048 Citations
  • 29 h-Index
20002023
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Research Output 2000 2019

2000
9 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
1 Citation (Scopus)

Estimates for non-resonant normal forms in hamiltonian perturbation theory

Valdinoci, E., 1 Nov 2000, In : Journal of Statistical Physics. 101, 3-4, p. 905-919 15 p.

Research output: Contribution to journalArticle

Small Divisors
Normal Form
Perturbation Theory
perturbation theory
Denominator
10 Citations (Scopus)
Hamiltonian Systems
Torus
Orbit
Unstable
orbits
2001
36 Citations (Scopus)

Upper bounds on Arnold diffusion times via Mather theory

Bessi, U., Chierchia, L. & Valdinoci, E., 1 Jan 2001, In : Journal des Mathematiques Pures et Appliquees. 80, 1, p. 105-129 25 p.

Research output: Contribution to journalArticle

Arnold Diffusion
Upper bound
Hamiltonians
Homoclinic
Ladders
2003
21 Citations (Scopus)

Elliptic Two-Dimensional Invariant Tori for the Planetary Three-Body Problem

Biasco, L., Chierchia, L. & Valdinoci, E., 1 Nov 2003, In : Archive for Rational Mechanics and Analysis. 170, 2, p. 91-135 45 p.

Research output: Contribution to journalArticle

Three-body Problem
Invariant Tori
Planets
Stars
Star
2004
14 Citations (Scopus)

Instability of resonant totally elliptic points of symplectic maps in dimension 4

Kaloshin, V., Mather, J. N. & Valdinoci, E., 1 Dec 2004, In : Asterisque. 297, p. 79-116 38 p.

Research output: Contribution to journalArticle

Lyapunov
Fixed point
Arnold Diffusion
Lyapunov Stability
Stability Theorem
3 Citations (Scopus)

Lack of integrability via viscosity solution methods

Gomes, D. A. & Valdinoci, E., 1 Dec 2004, In : Indiana University Mathematics Journal. 53, 4, p. 1055-1071 17 p.

Research output: Contribution to journalArticle

Integrable Hamiltonian System
Rotation number
Viscosity Solutions
Integrability
34 Citations (Scopus)
Periodic Media
Jet Flow
Ginzburg-Landau
Minimizer
Quasiperiodicity
2005
15 Citations (Scopus)

Density estimates for a degenerate/singular phase-transition model

Petrosyan, A. & Valdinoci, E., 1 Aug 2005, In : SIAM Journal on Mathematical Analysis. 36, 4, p. 1057-1079 23 p.

Research output: Contribution to journalArticle

Density Estimates
Transition Model
Minimizer
Phase Transition
Phase transitions
13 Citations (Scopus)

Geometric properties of Bernoulli-type minimizers

Petrosyan, A. & Valdinoci, E., 1 Jan 2005, In : Interfaces and Free Boundaries. 7, 1, p. 55-78 24 p.

Research output: Contribution to journalArticle

free boundaries
gradients
estimates
16 Citations (Scopus)

Mean curvature properties for p-Laplace phase transitions

Sciunzi, B. & Valdinoci, E., 1 Jan 2005, In : Journal of the European Mathematical Society. 7, 3, p. 319-359 41 p.

Research output: Contribution to journalArticle

Mean Curvature
Laplace
Phase Transition
Phase transitions
Viscosity
2006
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
2 Citations (Scopus)
37 Citations (Scopus)

Flat level set regularity of p-Laplace phase transitions

Valdinoci, E., Sciunzi, B. & Savin, V. O., 1 Jul 2006, In : Memoirs of the American Mathematical Society. 182, 858, p. 1-150 150 p.

Research output: Contribution to journalArticle

Laplace
Level Set
Phase Transition
Phase transitions
Regularity
6 Citations (Scopus)

Flatness of Bernoulli jets

Valdinoci, E., 1 Oct 2006, In : Mathematische Zeitschrift. 254, 2, p. 257-298 42 p.

Research output: Contribution to journalArticle

Flatness
Minimizer
Variational Problem
Bernoulli
Level Set
20 Citations (Scopus)

N-dimensional elliptic invariant tori for the planar (N + 1)-body problem

Biasco, L., Chierchia, L. & Valdinoci, E., 1 Jan 2006, In : SIAM Journal on Mathematical Analysis. 37, 5, p. 1560-1588 29 p.

Research output: Contribution to journalArticle

Invariant Tori
Orbits
Averaging Theory
KAM Theory
Solar system
2007
12 Citations (Scopus)

Critical points inside the gaps of ground state laminations for some models in statistical mechanics

De La Llave, R. & Valdinoci, E., 1 Oct 2007, In : Journal of Statistical Physics. 129, 1, p. 81-119 39 p.

Research output: Contribution to journalArticle

Lamination
statistical mechanics
Statistical Mechanics
laminates
Ground State
13 Citations (Scopus)

Entropy penalization methods for Hamilton-Jacobi equations

Gomes, D. A. & Valdinoci, E., 20 Oct 2007, In : Advances in Mathematics. 215, 1, p. 94-152 59 p.

Research output: Contribution to journalArticle

Open Access
Penalization Method
Entropy Method
Hamilton-Jacobi Equation
Evolution Equation
Linear equation
23 Citations (Scopus)

Ground states and critical points for generalized Frenkel-Kontorova models in ℤd

De La Llave, R. & Valdinoci, E., 1 Dec 2007, In : Nonlinearity. 20, 10, p. 2409-2424 16 p.

Research output: Contribution to journalArticle

Frenkel-Kontorova Model
Ground state
Ground State
Critical point
critical point
28 Citations (Scopus)

Multiplicity results for interfaces of Ginzburg-Landau-Allen-Cahn equations in periodic media

de la Llave, R. & Valdinoci, E., 20 Oct 2007, In : Advances in Mathematics. 215, 1, p. 379-426 48 p.

Research output: Contribution to journalArticle

Open Access
Allen-Cahn Equation
Periodic Media
Ginzburg-Landau Equation
Multiplicity Results
Minimizer
9 Citations (Scopus)

The geometry of mesoscopic phase transition interfaces

Novaga, M. & Valdinoci, E., 1 Dec 2007, In : Discrete and Continuous Dynamical Systems. 19, 4, p. 777-798 22 p.

Research output: Contribution to journalArticle

Phase Transition
Phase transitions
Density Estimates
Minimal Solution
Geometry
2008
100 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
14 Citations (Scopus)

Geometry of quasiminimal phase transitions

Farina, A. & Valdinoci, E., 1 Sep 2008, In : Calculus of Variations and Partial Differential Equations. 33, 1, p. 1-35 35 p.

Research output: Contribution to journalArticle

Level Set
Phase Transition
Phase transitions
Viscosity
Geometry
2 Citations (Scopus)

On periodic elliptic equations with gradient dependence

Berti, M., Matzeu, M. & Valdinoci, E., 1 May 2008, In : Communications on Pure and Applied Analysis. 7, 3, p. 601-615 15 p.

Research output: Contribution to journalArticle

Entire Solution
Periodic Functions
Elliptic Equations
Superposition
Slope
10 Citations (Scopus)

The Ginzburg-Landau equation in the Heisenberg group

Birindelli, I. & Valdinoci, E., 1 Oct 2008, In : Communications in Contemporary Mathematics. 10, 5, p. 671-719 49 p.

Research output: Contribution to journalArticle

Ginzburg-Landau Equation
Heisenberg Group
Level Set
Phase transitions
Minimizer
2009
26 Citations (Scopus)
Type Theory
Partial differential equation
Differential equation
Quasi-periodic Solutions
Elliptic PDE
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
19 Citations (Scopus)

Elliptic PDEs with fibered nonlinearities

Savin, O. & Valdinoci, E., 1 Apr 2009, In : Journal of Geometric Analysis. 19, 2, p. 420-432 13 p.

Research output: Contribution to journalArticle

Geometric Inequalities
Elliptic PDE
Bounded Solutions
Nonlinearity
Symmetry
6 Citations (Scopus)

Fibered nonlinearities for p(x)-Laplace equations

Chermisi, M. & Valdinoci, E., 1 Apr 2009, In : Advances in Calculus of Variations. 2, 2, p. 185-205 21 p.

Research output: Contribution to journalArticle

Geometric Inequalities
Laplace equation
Laplace's equation
Nonlinearity
Symmetry
139 Citations (Scopus)

Fractional Laplacian phase transitions and boundary reactions: A geometric inequality and a symmetry result

Sire, Y. & Valdinoci, E., 15 Mar 2009, In : Journal of Functional Analysis. 256, 6, p. 1842-1864 23 p.

Research output: Contribution to journalArticle

Geometric Inequalities
Fractional Laplacian
Nonlocal Equations
Phase Transition
Symmetry
8 Citations (Scopus)

Geometric pdes in the grushin plane: Weighted inequalities and flatness of level sets

Ferrari, F. & Valdinoci, E., 1 Dec 2009, In : International Mathematics Research Notices. 2009, 22, p. 4232-4270 39 p.

Research output: Contribution to journalArticle

Weighted Inequalities
Stable Solution
Flatness
Level Set
Partial differential equation
43 Citations (Scopus)

Liouville results for m-Laplace equations of Lane-Emden-Fowler type

Damascelli, L., Farina, A., Sciunzi, B. & Valdinoci, E., 1 Jan 2009, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 26, 4, p. 1099-1119 21 p.

Research output: Contribution to journalArticle

Sign-changing Solutions
Laplace's equation
3 Citations (Scopus)

Multibump solutions and asymptotic expansions for mesoscopic Allen-Cahn type equations

Novaga, M. & Valdinoci, E., 1 Oct 2009, In : ESAIM - Control, Optimisation and Calculus of Variations. 15, 4, p. 914-933 20 p.

Research output: Contribution to journalArticle

Multibump Solutions
Periodic Media
Asymptotic Expansion
Phase Transition
Phase transitions
15 Citations (Scopus)

Rigidity results for some boundary quasilinear phase transitions

Sire, Y. & Valdinoci, E., 1 Jul 2009, In : Communications in Partial Differential Equations. 34, 7, p. 765-784 20 p.

Research output: Contribution to journalArticle

Rigidity
Byproducts
Phase Transition
Phase transitions
Nonlinearity
4 Citations (Scopus)

Semilinear PDEs in the Heisenberg group: The role of the right invariant vector fields

Birindelli, I., Ferrari, F. & Valdinoci, E., 15 Jan 2009, In : Nonlinear Analysis, Theory, Methods and Applications. 72, 2, p. 987-997 11 p.

Research output: Contribution to journalArticle

Heisenberg Group
Semilinear
Vector Field
Invariant
Stable Solution
4 Citations (Scopus)

Some connections between results and problems of de Giorgi, moser and bangert

Junginger-Gestrich, H. & Valdinoci, E., 1 May 2009, In : Zeitschrift Fur Angewandte Mathematik und Physik. 60, 3, p. 393-401 9 p.

Research output: Contribution to journalArticle

Minimal Solution
Self-intersection
Integrand
rigidity
Rigidity
13 Citations (Scopus)

Some weighted Poincaré inequalities

Ferrari, F. & Valdinoci, E., 8 Oct 2009, In : Indiana University Mathematics Journal. 58, 4, p. 1619-1637 19 p.

Research output: Contribution to journalArticle

Weighted Inequalities
Euclidean space
Sub-Laplacian
Stable Solution
Heisenberg Group
8 Citations (Scopus)

Symmetry for a Dirichlet-Neumann problem arising in water waves

De La Llave, R. & Valdinoci, E., 1 Sep 2009, In : Mathematical Research Letters. 16, 5, p. 909-918 10 p.

Research output: Contribution to journalArticle

Water Waves
Neumann Problem
Dirichlet Problem
Dirichlet
Euclidean
41 Citations (Scopus)

The state of the art for a conjecture of de giorgi and related problems

Farina, A. & Valdinoci, E., 1 Jan 2009, Recent Progress on Reaction-Diffusion Systems and Viscosity Solutions. World Scientific Publishing, p. 74-96 23 p.

Research output: Chapter in Book/Conference paperChapter

2010
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
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
5 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
51 Citations (Scopus)

Flattening results for elliptic PDEs in unbounded domains with applications to overdetermined problems

Farina, A. & Valdinoci, E., 1 Mar 2010, In : Archive for Rational Mechanics and Analysis. 195, 3, p. 1025-1058 34 p.

Research output: Contribution to journalArticle

Overdetermined Problems
Geometric Inequalities
Geometric Analysis
Gradient Estimate
Elliptic PDE
18 Citations (Scopus)

Ground states and critical points for Aubry-Mather theory in statistical mechanics

De La Llave, R. & Valdinoci, E., 1 Apr 2010, In : Journal of Nonlinear Science. 20, 2, p. 153-218 66 p.

Research output: Contribution to journalArticle

Statistical mechanics
Statistical Mechanics
Ground state
Ground State
Critical point
13 Citations (Scopus)

On a Poincaré type formula for solutions of singular and degenerate elliptic equations

Farina, A., Sciunzi, B. & Valdinoci, E., 1 Jul 2010, In : Manuscripta Mathematica. 132, 3, p. 335-342 8 p.

Research output: Contribution to journalArticle

Singular Elliptic Equation
Degenerate Elliptic Equations
Stable Solution
Integrability
Refinement
12 Citations (Scopus)

Overdetermined problems in unbounded domains with Lipschitz singularities

Farina, A. & Valdinoci, E., 1 Jan 2010, In : Revista Matematica Iberoamericana. 26, 3, p. 965-974 10 p.

Research output: Contribution to journalArticle

Overdetermined Problems
Geometric Inequalities
Unbounded Domain
Lipschitz
Deduce
2 Citations (Scopus)

Some elliptic PDEs on riemannian manifolds with boundary

Sire, Y. & Valdinoci, E., 28 Dec 2010, In : Pacific Journal of Mathematics. 248, 2, p. 475-492 18 p.

Research output: Contribution to journalArticle

Elliptic PDE
Manifolds with Boundary
Riemannian Manifold
Nonlocal Equations
Stable Solution
2011
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
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
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