25 citations · 55 across the 14 of their papers we have counts for
17 papers
On the triple junction problem with general surface tension coefficients
Nicholas D. Alikakos, Zhiyuan Geng
We investigate the Allen-Cahn system \begin{equation*} Δu-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2, \end{equation*} where is a pote…
On the triple junction problem on the plane without symmetry hypotheses
Nicholas D. Alikakos, Zhiyuan Geng
We investigate the Allen-Cahn system \begin{equation*} Δu-W_u(u)=0,\quad u:\mathbb{R}^2\rightarrow\mathbb{R}^2, \end{equation*} where is a pote…
Identifying the Relationship between Seasonal Variation in Residential Load and Socioeconomic Characteristics
Zhenyu Wang, Hao Wang
Smart meter data analysis can provide insights into residential electricity consumption behaviors. Seasonal variation in consumption is not well understood but yet important to uti…
Entire minimizers of Allen-Cahn systems with sub-quadratic potentials
Nicholas D. Alikakos, Dimitrios Gazoulis, Arghir Zarnescu
We study entire minimizers of the Allen-Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with sub-quadratic behaviour local…
On Almost Entire Solutions Of The Burgers Equation
Nicholas Alikakos, Dimitrios Gazoulis
Solutions that satisfy classically the Burgers equation except, perhaps, on a closed set S of the plane of potential singularities whose Hausdorff 1-measure is zero, ,…
Stability Criteria for Multiphase Partitioning Problems with Volume Constraints
N. D. Alikakos, A. C. Faliagas
We study the stability of partitions involving two or more phases in convex domains under the assumption of at most two-phase contact, thus excluding in particular triple junctions…
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…
On the structure of phase transition maps for three or more coexisting phases
Nicholas D. Alikakos
This paper is partly based on a lecture delivered by the author at the ERC workshop "Geometric Partial Differential Equations" held in Pisa in September 2012. What is presented her…
Plateau angle conditions for the vector-valued Allen-Cahn equation
Nicholas D. Alikakos, Panagiotis Antonopoulos, Apostolos Damialis
Under proper hypotheses, we rigorously derive the Plateau angle conditions at triple junctions of diffused interfaces in three dimensions, starting from the vector-valued Allen-Cah…
A new proof for the existence of an equivariant entire solution connecting the minima of the potential for the system Δu - W_u (u) = 0
Nicholas D. Alikakos
Recently, Giorgio Fusco and the author studied the system Δu - W_u (u) = 0 for a class of potentials that possess several global minima and are invariant under a general finite ref…
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.
Some basic facts on the system Δu - W_u (u) = 0
Nicholas D. Alikakos
We rewrite the system Δu - W_u (u) = 0, for u: R^n to R^n, in the form div T = 0, where T is an appropriate stress-energy tensor, and derive certain a priori consequences on the so…
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…
Heteroclinic Travelling Waves of Gradient Diffusion Systems
N. I. Katzourakis, N. D. Alikakos
We establish existence of travelling waves to the gradient system connecting two minima of when $u : \R \times (0,\infty) \larrow \R^N$, that is, w…