Rigidity of minimizers in nonlocal phase transitions

Abstract

We obtain the classification of certain global bounded solutions for semilinear nonlocal equations of the type

$${△}^{s}u=W^{\prime }\left(u\right)\text{ in }{ℝ}^n,\text{ with }s\in \left(\frac{1}{2},1\right),$$

where $W$ is a double-well potential.