Year: 2019
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 1 : pp. 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.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.OA-0008
Analysis in Theory and Applications, Vol. 35 (2019), Iss. 1 : pp. 1–27
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: De Giorgi’s conjecture fractional Laplacian.