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arXiv · 1711.03215

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

Hardy Chan·Yong Liu·Juncheng Wei
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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.

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Hardy Chan, Yong Liu, Juncheng Wei. 2017-11-09. Existence and instability of deformed catenoidal solutions for fractional Allen--Cahn equation. https://arxiv.org/abs/1711.03215

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