TY - JOUR
T1 - Rigidity of Minimizers in Nonlocal Phase Transitions II
AU - O. Savin
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 - <p style="text-align: justify;">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 $$\Delta ^{\frac 12} u=W&#39;(u) \quad \mbox{in}\quad&nbsp; \mathbb{R}^n,$$where $W$ is a double well potential.<br/></p>