Layered solutions to the vector Allen-Cahn equation in $R^2$. Characterization of minimizers and a new approach to heteroclinic connections

Giorgio Fusco

Let $W:R^m\to R$ be a nonnegative potential with exactly two nondegenerate zeros $a_{-}\ne a_{+}\in R^m$. We assume that there are$N\ge 1$ distinct heteroclinic orbits conne…