Minimizers for a fractional Allen-Cahn equation in a periodic medium

TL;DR

This paper investigates minimal solutions of a fractional Allen-Cahn equation in a periodic medium, focusing on the geometric properties of interfaces and constructing minimal interfaces with specific directional and width constraints.

Contribution

It introduces a new analysis of minimal solutions and constructs minimal interfaces with prescribed direction and universal width in a fractional phase transition model.

Findings

Characterization of geometric properties of minimal interfaces

Construction of minimal interfaces with prescribed direction

Existence of universal width minimal interfaces

Abstract

We aim to study the solutions of a fractional mesoscopic model of phase transitions in a periodic medium. After investigating the geometric properties of the interface of the associated minimal solutions, we construct minimal interfaces lying to a strip of prescribed direction and universal width.