11 citations · 22 across the 14 of their papers we have counts for
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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…
Minimizing under relaxed symmetry constraints: Triple and -junctions
Giorgio Fusco
We consider a nonnegative potential invariant under the action of the rotation group of the regular polygon with sides, . W…
Periodic motions for multi-wells potentials and layers dynamic for the vector Allen-Cahn equation
Giorgio Fusco
We consider a nonnegative potential 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…
Layered solutions to the vector Allen-Cahn equation in . Characterization of minimizers and a new approach to heteroclinic connections
Giorgio Fusco
Let be a nonnegative potential with exactly two nondegenerate zeros . We assume that there are distinct heteroclinic orbits conne…
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 of the vector Allen-Cahn equation , where is smooth,…
On the asymptotic behavior of symmetric solutions of the Allen-Cahn equation in unbounded domains in
Giorgio Fusco, Francesco Leonetti, Cristina Pignotti
We consider a Dirichlet problem for the Allen-Cahn equation in a smooth, bounded or unbounded, domain Under suitable assumptions, we prove an existence result…
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.
Asymptotic behavior and rigidity results for symmetric solutions of the elliptic system
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.
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…
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.
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…
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…