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 non-local mean curvature.
Solutions of the fractional Allen-Cahn equations invariant under screw motion / Cinti E; Davila J; Del Pino M. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - STAMPA. - 94:(2016), pp. 295-313. [10.1112/jlms/jdw033]
Solutions of the fractional Allen-Cahn equations invariant under screw motion
CINTI, ELEONORA;
2016
Abstract
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 non-local mean curvature.File in questo prodotto:
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