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