WIAS Preprint No. 2155, (2015)

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


  • Cinti, Eleonora
  • Davila, Juan
  • Del Pino, Manuel

2010 Mathematics Subject Classification

  • 35J61 35J20 35B08 47J30


  • Fractional Laplacian, entire solutions, nonlocal perimeter


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

Appeared in

  • J. London Math. Soc. (2), 94 (2016) pp. 295--313.

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