Solution of the fractional Allen-Cahn equation which are invariant under screw motion
classification
🧮 math.AP
keywords
allen-cahnequationfractionalhelicoidsinvariantunderadditioncurvature
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We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in $\mathbb R^3$, 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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