Multiplicity of critical points for the fractional Allen-Cahn energy

TL;DR

This paper investigates the fractional Allen-Cahn energy in bounded domains, demonstrating that it possesses infinitely many critical points as the perturbation parameter approaches zero.

Contribution

It introduces the fractional analogue of the Allen-Cahn energy and proves the existence of infinitely many critical points in this setting.

Findings

Number of critical points tends to infinity as perturbation parameter approaches zero

Fractional Allen-Cahn energy admits multiple critical points in bounded domains

Critical points' multiplicity increases with decreasing perturbation parameter

Abstract

In this paper we study the fractional analogue of the Allen-Cahn energy in bounded domains, and we show that it admits a number of critical points which goes to infinity as the perturbation parameter tends to zero.