Entire solutions to equivariant elliptic systems with variational\n structure

2008/11/03 by Nicholas D. Alikakos, Alikakos, Nicholas D., Giorgio Fusco +1 · 1 citation
Computer Science · Mathematics · #35J45 #35J50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0811.0106

openalex publication_date 2008/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we consider the system \Δu - W_u (u) = 0, where u:\nRⁿ to Rⁿ, for a class of potentials W: Rⁿ to R that possess several global\nminima and are invariant under a general finite reflection group G. We\nestablish existence of nontrivial entire solutions connecting the global minima\nof W along certain directions at infinity.\n

Citations

• Self similar expanding solutions of the planar network flow
• Mean Curvature Motion of Graphs with Constant Contact Angle and Moving Boundaries

Cited by

• Self-Expanding Solutions to the Mean Curvature Flow for Multiphase Surfaces with Regular Junctions

Related

• 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
• On an elliptic system with symmetric potential possessing two global minima
• Existence of entire solutions for some elliptic systems
• Abundance of entire solutions to nonlinear elliptic equations by the variational method
• A Liouville type result for bounded, entire solutions to a class of variational semilinear elliptic systems