Rigidity of Minimizers in Nonlocal Phase Transitions II (Analysis in Theory and Applications, 2022)
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 $$Δ ^{\frac 12} u=W'(u) \quad in\quad \mathbb{R}^n,$$where $W$ is a double well potential.
Keywords: De Giorgi’s conjecture; fractional Laplacian.