Rigidity of Minimizers in Nonlocal Phase Transitions II

Abstract

In this paper we extend the results of [12] to the borderline case $s = \frac 12$. We obtain the classification of global bounded solutions with asymptotically flat level sets for semilinear nonlocal equations of the type $$\Delta ^{\frac 12} u=W'(u) \quad \mbox{in}\quad  \mathbb{R}^n,$$where $W$ is a double well potential.