Volume 35, Issue 1
Rigidity of Minimizers in Nonlocal Phase Transitions II

O. Savin

10.4208/ata.OA-0008

Anal. Theory Appl., 35 (2019), pp. 1-27.

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  • 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 $$\Delta ^{\frac 12} u=W'(u) \quad \mbox{in}\quad \ R^n,$$where $W$ is a double well potential.


  • AMS Subject Headings

35J61

Published online: 2019-04