TY - JOUR T1 - Rigidity of Minimizers in Nonlocal Phase Transitions II JO - Analysis in Theory and Applications VL - 1 SP - 1 EP - 27 PY - 2019 DA - 2019/04 SN - 35 DO - http://doi.org/10.4208/ata.OA-0008 UR - https://global-sci.org/intro/article_detail/ata/13090.html KW - De Giorgi’s conjecture, fractional Laplacian. AB -

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.