@Article{ATA-35-1, author = {O. Savin}, title = {Rigidity of Minimizers in Nonlocal Phase Transitions II}, journal = {Analysis in Theory and Applications}, year = {2019}, volume = {35}, number = {1}, pages = {1--27}, 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.