• 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

2013
7 Citations (Scopus)

Geometric analysis of fractional phase transition interfaces

Franzina, G. & Valdinoci, E., 1 Jan 2013, In : Springer INdAM Series. 2, p. 117-130 14 p.

Research output: Contribution to journalArticle

Geometric Analysis
Fractional
Phase Transition
Transition Model
Operator
126 Citations (Scopus)

Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators

Servadei, R. & Valdinoci, E., 19 Sep 2013, In : Revista Matematica Iberoamericana. 29, 3, p. 1091-1126 36 p.

Research output: Contribution to journalArticle

Variational Inequalities
Operator
Estimate
Fractional Laplacian
Integro-differential Operators
12 Citations (Scopus)

On partially and globally overdetermined problems of elliptic type

Farina, A. & Valdinoci, E., 1 Jan 2013, In : American Journal of Mathematics. 135, 6, p. 1699-1726 28 p.

Research output: Contribution to journalArticle

Overdetermined Problems
Overdetermined Systems
Elliptic PDE
Shape Optimization
Rigidity
1 Citation (Scopus)

Pointwise estimates and monotonicity formulas without maximum principle

Montenegro, M. & Valdinoci, E., 29 Apr 2013, In : Journal of Convex Analysis. 20, 1, p. 199-220 22 p.

Research output: Contribution to journalArticle

Monotonicity Formula
Pointwise Estimates
Elliptic Partial Differential Equations
Maximum Principle
Monotonicity
2 Citations (Scopus)

Pointwise estimates and rigidity results for entire solutions of nonlinear elliptic pde's

Farina, A. & Valdinoci, E., 1 Apr 2013, In : ESAIM - Control, Optimisation and Calculus of Variations. 19, 2, p. 616-627 12 p.

Research output: Contribution to journalArticle

Nonlinear Elliptic PDE
Entire Solution
Pointwise Estimates
Rigidity
Elliptic Operator
45 Citations (Scopus)

Regularity of nonlocal minimal cones in dimension 2

Savin, O. & Valdinoci, E., 1 Sep 2013, In : Calculus of Variations and Partial Differential Equations. 48, 1-2, p. 33-39 7 p.

Research output: Contribution to journalArticle

Cones
Cone
Regularity
Singular Set
Minimal surface
28 Citations (Scopus)

Regularity properties of nonlocal minimal surfaces via limiting arguments

Caffarelli, L. & Valdinoci, E., 25 Nov 2013, In : Advances in Mathematics. 248, p. 843-871 29 p.

Research output: Contribution to journalArticle

Open Access
Regularity Properties
Minimal surface
Limiting
Flatness
Fractional
16 Citations (Scopus)

Some monotonicity results for minimizers in the calculus of variations

Savin, O. & Valdinoci, E., 15 May 2013, In : Journal of Functional Analysis. 264, 10, p. 2469-2496 28 p.

Research output: Contribution to journalArticle

Open Access
Stable Solution
Calculus of variations
Minimizer
Global Solution
Rigidity
20 Citations (Scopus)

Splitting Theorems, Symmetry Results and Overdetermined Problems for Riemannian Manifolds

Farina, A., Mari, L. & Valdinoci, E., Oct 2013, In : Communications in Partial Differential Equations. 38, 10, p. 1818-1862 45 p.

Research output: Contribution to journalArticle

Overdetermined Problems
Elliptic Problems
Riemannian Manifold
Killing Vector Field
Symmetry
20 Citations (Scopus)

Stable solutions of elliptic equations on Riemannian manifolds

Farina, A., Sire, Y. & Valdinoci, E., 1 Jul 2013, In : Journal of Geometric Analysis. 23, 3, p. 1158-1172 15 p.

Research output: Contribution to journalArticle

Weighted Inequalities
Stable Solution
Smooth Manifold
Flatness
Elliptic Partial Differential Equations
321 Citations (Scopus)

Variational methods for non-local operators of elliptic type

Servadei, R. & Valdinoci, E., 1 May 2013, In : Discrete and Continuous Dynamical Systems- Series A. 33, 5, p. 2105-2137 33 p.

Research output: Contribution to journalArticle

Open Access
Variational Methods
Mathematical operators
Critical point
Nonlinear analysis
Operator
2012
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
5 Citations (Scopus)
Open Access
Degenerate Problems
Gradient Estimate
Pointwise Estimates
Nonnegative Curvature
Unbounded Domain

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
4 Citations (Scopus)

Density estimates for phase transitions with a trace

Sire, Y. & Valdinoci, E., 27 Aug 2012, In : Interfaces and Free Boundaries. 14, 2, p. 153-165 13 p.

Research output: Contribution to journalArticle

ellipticity
estimates
1260 Citations (Scopus)

Hitchhiker's guide to the fractional Sobolev spaces

Di Nezza, E., Palatucci, G. & Valdinoci, E., 1 Jul 2012, In : Bulletin des Sciences Mathematiques. 136, 5, p. 521-573 53 p.

Research output: Contribution to journalArticle

Open Access
Sobolev Spaces
Fractional
Compact Embedding
Non-Lipschitz
Besov Spaces

Minimizers of a variational problem inherit the symmetry of the domain

Montenegro, M. & Valdinoci, E., 21 Aug 2012, In : Electronic Journal of Differential Equations. 2012, p. 1-6 6 p.

Research output: Contribution to journalArticle

Open Access
Moving Planes
Minimizer
Variational Problem
Symmetry
Framework
328 Citations (Scopus)

Mountain Pass solutions for non-local elliptic operators

Servadei, R. & Valdinoci, E., 15 May 2012, In : Journal of Mathematical Analysis and Applications. 389, 2, p. 887-898 12 p.

Research output: Contribution to journalArticle

Open Access
Mountain Pass
Elliptic Operator
Integro-differential Operators
Mathematical operators
Boundary conditions
9 Citations (Scopus)

Partially and globally overdetermined problems of elliptic type

Farina, A. & Valdinoci, E., 1 Jan 2012, In : Advances in Nonlinear Analysis. 1, 1, p. 27-45 19 p.

Research output: Contribution to journalArticle

Overdetermined Problems
Unbounded Domain
Bounded Domain
Review
5 Citations (Scopus)

Some results on minimizers and stable solutions of a variational problem

Farina, A. & Valdinoci, E., 1 Aug 2012, In : Ergodic Theory and Dynamical Systems. 32, 4, p. 1302-1312 11 p.

Research output: Contribution to journalArticle

Stable Solution
Minimizer
Variational Problem
Monotonicity
Symmetry
10 Citations (Scopus)

Stable solutions of elliptic equations on Riemannian manifolds with Euclidean coverings

Farina, A., Sire, Y. & Valdinoci, E., 1 Jan 2012, In : Proceedings of the American Mathematical Society. 140, 3, p. 927-930 4 p.

Research output: Contribution to journalArticle

Stable Solution
Elliptic Partial Differential Equations
Bounded Solutions
Semilinear
Level Set
53 Citations (Scopus)

Γ-convergence for nonlocal phase transitions

Savin, O. & Valdinoci, E., 1 Jan 2012, In : Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire. 29, 4, p. 479-500 22 p.

Research output: Contribution to journalArticle

Open Access
Minimal surface
Phase Transition
Converge
Double-well Potential
Energy
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

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
5 Citations (Scopus)

Closed curves of prescribed curvature and a pinning effect

Novaga, M. & Valdinoci, E., 1 Mar 2011, In : Networks and Heterogeneous Media. 6, 1, p. 77-88 12 p.

Research output: Contribution to journalArticle

Closed curve
Curvature
Periodic Media
Periodic Forcing
Forcing Term
6 Citations (Scopus)

Curve shortening flow in heterogeneous media

Cesaroni, A., Novaga, M. & Valdinoci, E., 19 Dec 2011, In : Interfaces and Free Boundaries. 13, 4, p. 485-505 21 p.

Research output: Contribution to journalArticle

curves
homogenizing
norms
curvature
estimates
1 Citation (Scopus)

Density estimates for a fluid jet model in the Heisenberg group

Ferrari, F. & Valdinoci, E., 1 Oct 2011, In : Journal of Mathematical Analysis and Applications. 382, 1, p. 448-468 21 p.

Research output: Contribution to journalArticle

Open Access
Density Estimates
Heisenberg Group
Fluid
Fluids
Free Boundary
19 Citations (Scopus)

Density estimates for a nonlocal variational model via the Sobolev inequality

Savin, O. & Valdinoci, E., 1 Dec 2011, In : SIAM Journal on Mathematical Analysis. 43, 6, p. 2675-2687 13 p.

Research output: Contribution to journalArticle

Variational Model
Density Estimates
Sobolev Inequality
Minimizer
Double-well Potential
1 Citation (Scopus)

Duality theory, representation formulas and uniqueness results for viscosity solutions of hamilton-jacobi equations

Gomes, D. A. & Valdinoci, E., 1 Jan 2011, In : Springer Proceedings in Mathematics. 2, p. 361-386 26 p.

Research output: Contribution to journalReview article

Infinite-horizon Problems
Relaxed Controls
Representation Formula
Duality Theory
Hamilton-Jacobi Equation
1 Citation (Scopus)

Lp-bounds for quasi-geostrophic equations via functional analysis

De La Llave, R. & Valdinoci, E., 4 Aug 2011, In : Journal of Mathematical Physics. 52, 8, 083101.

Research output: Contribution to journalArticle

functional analysis
Quasi-geostrophic Equations
Functional Analysis
Operator Splitting Method
Product formula
1 Citation (Scopus)

On the allen-cahn equation in the grushin plane: A monotone entire solution that is not one-dimensional

Birindelli, I. & Valdinoci, E., 1 Mar 2011, In : Discrete and Continuous Dynamical Systems. 29, 3, p. 823-838 16 p.

Research output: Contribution to journalArticle

Allen-Cahn Equation
Entire Solution
Energy Estimates
Counterexample
Monotone
11 Citations (Scopus)

Rigidity results for elliptic PDEs with uniform limits: An abstract framework with applications

Farina, A. & Valdinoci, E., 1 Dec 2011, In : Indiana University Mathematics Journal. 60, 1, p. 121-141 21 p.

Research output: Contribution to journalArticle

Elliptic PDE
Fully Nonlinear
Nonlinear Operator
Laplace Operator
Elliptic Operator
82 Citations (Scopus)

Uniform estimates and limiting arguments for nonlocal minimal surfaces

Caffarelli, L. & Valdinoci, E., 1 May 2011, In : Calculus of Variations and Partial Differential Equations. 41, 1-2, p. 203-240 38 p.

Research output: Contribution to journalArticle

Uniform Estimates
Minimal surface
Perimeter
Limiting
Minimal Set
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
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