Giorgio Fusco

collaborators

4 papers

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

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.

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

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

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 $Δ u = W_{u} (u)$