Entire solutions to equivariant elliptic systems with variational structure

Abstract

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 a general finite reflection group G. We establish existence of nontrivial entire solutions connecting the global minima of W along certain directions at infinity.

28 pages, 2 figures; major revision

References in corpus (3)

• Self similar expanding solutions of the planar network flow
• On an elliptic system with symmetric potential possessing two global minima
• Mean Curvature Motion of Graphs with Constant Contact Angle and Moving Boundaries