Asymptotic behavior of the free interface for entire vector minimizers in phase transitions

Nicholas D. Alikakos, Zhiyuan Geng, Arghir Zarnescu

We study globally bounded entire minimizers $u:{\mathbb{R}}^n\to {\mathbb{R}}^m$ of Allen-Cahn systems for potentials $W\ge 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim |u-a…