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

Published 9 Nov 2017 in math.AP | (1711.03215v2)

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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