arXiv:1711.03215 Abstract | arXiv Analytics

arXiv:1711.03215 [math.AP]Abstract References Reviews Resources

A gluing construction for fractional elliptic equations. Part I: a model problem on the catenoid

Published 2017-11-09Version 1

We develop a new infinite dimensional gluing method for fractional elliptic equations. In Part I, as a model problem, we construct a solution of the fractional Allen--Cahn equation vanishing on a rotationally symmetric surface which resembles a catenoid and has sub-linear growth at infinity. In Part II, we construct counter-examples to De Giorgi Conjecture for the fractional Allen--Cahn equation.

Categories: math.AP

Keywords: fractional elliptic equations, model problem, gluing construction, infinite dimensional gluing method, fractional allen-cahn equation vanishing

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