. A P ] 9 N ov 2 01 7 A GLUING CONSTRUCTION FOR FRACTIONAL ELLIPTIC EQUATIONS . PART I : A MODEL PROBLEM ON THE CATENOID
نویسنده
چکیده
Abstract. 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 counterexamples to De Giorgi Conjectures to fractional Allen-Cahn equation.
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