Allen-Cahn Solutions with Triple Junction Structure at Infinity

Étienne Sandier, Peter Sternberg

We construct an entire solution $U:{\mathbb{R}}^2\to {\mathbb{R}}^2$ to the elliptic system \[ ΔU=\nabla_uW(U), \] where $W:{\mathbb{R}}^2\to [0,\infty )$ is a `triple-well' potential. Th…