Existence and instability of deformed catenoidal solutions for fractional Allen--Cahn equation

Abstract

We develop a new infinite dimensional gluing method for fractional elliptic equations. As a model problem, we construct solutions of the fractional Allen--Cahn equation vanishing on a rotationally symmetric surface which resembles a catenoid and have sub-linear growth at infinity. Moreover, such solutions are unstable.

This is a revised and expanded version of the previous article titled "A gluing construction for fractional elliptic equations. Part I: a model problem on the catenoid"

References in corpus (3)

• Anisotropic fractional perimeters
• Stable $s$-minimal cones in ${\mathbb{R}}^3$ are flat for $s\sim 1$
• Multiplicity of critical points for the fractional Allen-Cahn energy

Cited by in corpus (1)

• Uniqueness of entire ground states for the fractional plasma problem