G. Fusco

activity

20082021

most citedOn an elliptic system with symmetric potential possessing two global minima

11 citations · 22 across the 14 of their papers we have counts for

collaborators

16 papers

math.AP2021★ 2 cited

Sharp lower bounds for vector Allen-Cahn energy and qualitative properties of minimizes under no symmetry hypotheses

Nicholas D. Alikakos, Giorgio Fusco

We study vector minimizers u of the Allen-Cahn functional with potentials possessing N global minima defined on bounded domains, with certain geometrical features and Dirichlet con…

math.AP2021

Minimizing under relaxed symmetry constraints: Triple and $N$ -junctions

Giorgio Fusco

We consider a nonnegative potential $W : R^{2} \to R$ invariant under the action of the rotation group $C_{N}$ of the regular polygon with $N$ sides, $N \geq 3$ . W…

math.AP2020

Periodic motions for multi-wells potentials and layers dynamic for the vector Allen-Cahn equation

Giorgio Fusco

We consider a nonnegative potential $W$ that vanishes on a finite set and study the existence of periodic orbits of the equation \[\ddot{u}=W_u(u),\;\;t\in\R,\] that have the prope…

math.DS2018★ 6 cited

Existence of periodic orbits near heteroclinic connections

Giorgio Fusco, Giovanni F. Gronchi, Matteo Novaga

We consider a potential $W : R^{m} \to R$ with two different global minima $a_{-}, a_{+}$ and, under a symmetry assumption, we use a variational approach to show that the Hamiltonia…

math.DS2017★ 1 cited

On the existence of connecting orbits for critical values of the energy

Giorgio Fusco, Giovanni F. Gronchi, Matteo Novaga

We consider an open connected set $Ω$ and a smooth potential $U$ which is positive in $Ω$ and vanishes on $\partial Ω$ . We study the existence of orbits of the mechanical system \[…

math.AP2016

Layered solutions to the vector Allen-Cahn equation in $R^{2}$ . Characterization of minimizers and a new approach to heteroclinic connections

Giorgio Fusco

Let $W : R^{m} \to R$ be a nonnegative potential with exactly two nondegenerate zeros $a_{-} \neq = a_{+} \in R^{m}$ . We assume that there are $N \geq 1$ distinct heteroclinic orbits conne…

math.AP2014

Multyphase solutions to the vector Allen-Cahn equation: Crystalline and other complex symmetric structures

Peter W. Bates, Giorgio Fusco, Panayotis Smyrnelis

We present a systematic study of entire symmetric solutions $u : R^{n} \to R^{m}$ of the vector Allen-Cahn equation $Δ u - W_{u} (u) = 0, x \in R^{n}$ , where $W : R^{m} \to R$ is smooth,…

math.AP2014

On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in $R^{2}$

Giorgio Fusco, Francesco Leonetti, Cristina Pignotti

We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain $Ω \subset R^{n} .$ Under suitable assumptions, we prove an existence result…

math.AP2014

Density estimates for vector minimizers and applications

Nicholas D. Alikakos, Giorgio Fusco

We extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions.

math.AP2014

Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system $Δ u = W_{u} (u)$

Nicholas D. Alikakos, Giorgio Fusco

We study symmetric vector minimizers of the Allen-Cahn energy and establish various results concerning their structure and their asymptotic behavior.

math.AP2013

A maximum principle for systems with variational structure and an application to standing waves

Nicholas D. Alikakos, Giorgio Fusco

We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differe…

math-ph2012★ 1 cited

Stationary motion of a self gravitating toroidal incompressible liquid layer

Giorgio Fusco, Piero Negrini, Waldyr M. Oliva

We consider an incompressible fluid contained in a toroidal stratum which is only subjected to Newtonian self-attraction. Under the assumption of infinitesimal tickness of the stra…

math.AP2010★ 1 cited

A replacement lemma for obtaining pointwise estimates in phase transition models

Nicholas D. Alikakos, Giorgio Fusco

We establish a replacement lemma for a variational problem, which is not based on a local argument. We then apply it to a phase transition problem and obtain pointwise estimates.

math.DS2009

Platonic Polyhedra, Topological Constraints and Periodic Solutions of the Classical $N$ -Body Problem

G. Fusco, G. F. Gronchi, P. Negrini

We prove the existence of a number of smooth periodic motions $u_{*}$ of the classical Newtonian $N$ -body problem which, up to a relabeling of the $N$ particles, are invariant under…

math.AP2008

Entire solutions to equivariant elliptic systems with variational structure

Nicholas D. Alikakos, Giorgio Fusco

In the present paper we consider the system Δu - W_u (u) = 0, where u: R^n to R^n, for a class of potentials W: R^n to R that possess several global minima and are invariant under…

math.AP2008★ 11 cited

On an elliptic system with symmetric potential possessing two global minima

Nicholas D. Alikakos, Giorgio Fusco

We consider the system Δu - W_u (u) = 0, for u: R^2 -> R^2, W: R^2 -> R, where W_u (u) is a smooth potential, symmetric with respect to the u_1, u_2 axes, possessing two global min…

Sharp lower bounds for vector Allen-Cahn energy and qualitative properties of minimizes under no symmetry hypotheses

Minimizing under relaxed symmetry constraints: Triple and N-junctions

Periodic motions for multi-wells potentials and layers dynamic for the vector Allen-Cahn equation

Existence of periodic orbits near heteroclinic connections

On the existence of connecting orbits for critical values of the energy

Layered solutions to the vector Allen-Cahn equation in R2. Characterization of minimizers and a new approach to heteroclinic connections

Multyphase solutions to the vector Allen-Cahn equation: Crystalline and other complex symmetric structures

On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in R2

Density estimates for vector minimizers and applications

Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system Δu=Wu​(u)

A maximum principle for systems with variational structure and an application to standing waves

Stationary motion of a self gravitating toroidal incompressible liquid layer

A replacement lemma for obtaining pointwise estimates in phase transition models

Platonic Polyhedra, Topological Constraints and Periodic Solutions of the Classical N-Body Problem

Entire solutions to equivariant elliptic systems with variational structure

On an elliptic system with symmetric potential possessing two global minima

Minimizing under relaxed symmetry constraints: Triple and $N$ -junctions

Layered solutions to the vector Allen-Cahn equation in $R^{2}$ . Characterization of minimizers and a new approach to heteroclinic connections

On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in $R^{2}$

Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system $Δ u = W_{u} (u)$

Platonic Polyhedra, Topological Constraints and Periodic Solutions of the Classical $N$ -Body Problem