Solution of the fractional Allen-Cahn equation which are invariant under screw motion

2015/09/02 by Eleonora Cinti, Juan Dávila, Juan Davila +5
Mathematics · #35J20 #35J61 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Meromorphic and Entire Functions #Nonlinear Partial Differential Equations #math.AP #msc:35J20 #msc:35J61

paper · pdf · doi:10.48550/arxiv.1509.00786

arxiv created 2015/09/02 · openalex publication_date 2015/09/02 · arxiv updated 2015/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in \mathbb R³, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature.

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